#cosecant notes

[er-cryptid]

[tutoroot]

What are the Standard Angles of Trigonometric Table? 

The Trigonometric Table is essentially a tabular compilation of trigonometric values and ratio for various conventional angles such as 0°, 30°, 45°, 60°, and 90°, often with extra angles such as 180°, 270°, and 360° included. Due to the existence of patterns within trigonometric ratios and even between angles, it is simple to forecast the values of the trigonometry table and to use the table as a reference to compute trigonometric values for many other angles. The sine function, cosine function, tan function, cot function, sec function, and cosec function are trigonometric functions.

The trigonometric table is helpful in a variety of situations. It is required for navigating, research, and architecture. This table was widely utilized in the pre-digital age, even before pocket calculators were available. The table also aided in the creation of the earliest mechanical computing machines. The Fast Fourier Transform (FFT) algorithms are another notable application of trigonometric tables.

Standard Angles of Trigonometric Table

The values of trigonometric ratios for the angles 0°, 30°, 45°, 60°, and 90° are widely utilized to answer trigonometry issues. These values are related to measuring the lengths and angles of a right-angle triangle. Hence, the standard angles in trigonometry are 0°, 30°, 45°, 60°, and 90°. Following are the trigonometry angle tables (show the figure).

The trigonometric table in its simplest sense refers to the collection of values of trigonometric functions of various standard angles including 0°, 30°, 45°, 60°, 90°, along with other angles such as 180°, 270°, and 360°. These angles are all included in the table. This makes it easier to determine and arrive at the values of the trigonometric ratios in a trigonometric table, also, the table can be used as a referral illustration to compute trigonometric values for various other angles, due to the patterns that are seen within the trigonometric ratios and those between angles.

The table as one might note, consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent. The short forms of these are very popular – sin, cos, tan, cosec, sec, and cot, respectively. Always, memorize the values of the trigonometric ratios of the standard angles.

Always remember these points in the trigonometric table:

In a trigonometric table, the trigonometric values for complementary angles, such as 30° and 60° are measured by applying complementary formulas for various trigonometric ratios.

The value for some ratios in a table is ∞ “not defined”. The reason is that while computing values, the denominator shows a “0”, which implies that the trigonometric value cannot be defined, and is as good to be the equivalent of infinity.

Please notice the sign change in the values at places under 180°, and 270°, for values of some trig ratios in a trigonometric table. This happens because there is a change in the quadrant.

Trigonometric values

As explained, if trigonometry deals with the relationship between the sides of a triangle (right-angled triangle) and its angles, then the trigonometric value refers to the values of different ratios, sine, cosine, tangent, secant, cotangent, and cosecant, all in the trigonometric table. All the trigonometric ratios are in relation with the sides of a right-angle triangle. The trigonometric values are derived applying these the ratios. Refer to the following steps to create trigonometric values:

Steps to Create Values for Trigonometry Table

Step 1: 

Make a table with the top row showing the angles such as 0°, 30°, 45°, 60°, and 90°, and the first column listing the trigonometric functions such as sin, cos, tan, cosec, sec, cot.  

Step 2: Determine the value of sin 

To find the sin values, divide 0, 1, 2, 3, 4 by 4 under the root, in that order.

Step 3: Determine the value of cos 

The cos-value is the inverse of the sin angle. To find the value of cos, divide by 4 in the opposite order as sin.

Step 4: Determine the value of tan 

Tan is defined as sin divided by cos. Tan equals sin/cos. Divide the value of sin at 0° by the value of cos at 0° to get the value of tan at 0°.

Step 5: Determine the value of cot 

The reciprocal of tan is the value of cot. Divide 1 by the value of tan at 0° to get the value of cot at 0°. As a result, the value will be as follows: cot 0° = 1/0 = Unlimited or Not Defined  

Step 6: Determine the value of cosec 

The reciprocal of sin at 0° is the value of cosec at 0°. 

Step 7: Determine the value of sec 

Any common values of cos may be used to calculate sec. The value of sec on 0° is the inverse of the value of cos on 0°.

While we learn trigonometric values of the trigonometry tables, it will also be interesting to take note of the application areas of the table. On a broader note, the trigonometric table is used in:

Science, technology, engineering, navigation, science and engineering. Before the advent of the digital era, the trigonometric table was very effective. In the course of time, the table helped in the conceptualization of mechanical computing devices. Trigonometric tables are also used in the Fast Fourier Transform (FFT) algorithms.

Important Tricks to Remember Trigonometry Table

Knowing the trigonometry table can help you answer trigonometry problems and remembering the trigonometry table for normal angles ranging from 0° to 90° is simple. Knowing the trigonometric formulae makes remembering the trigonometry table much easier. The trigonometry formulae are required for the Trigonometry ratios table.

The angle values of trigonometric functions, cotangent, secant, and cosecant are computed by applying these standard angle values of sine, cosecant, and tangent. All the higher angle values of trigonometric functions such as 120°, and 360°, are easier to compute, through the standard angle values in a trigonometric values table.

If you still can’t remember the values of Trigonometry tables, consider Tutoroot personalised sessions. Our Maths online Tuition session will help you clearly understand the table along with tricks to memorize. 

[sstonki]

Exponential graph equation maker

Note that the first function is sin(a*x). You can also enter an exact value into the box at the top of the slider, followed by the GRAPH button or the Enter key.įor example, in the chart above, press 'reset'. When you enter your equations, you can refer to up to four variables that are controlled by sliders.Īnd you can adjust the value of each variable by moving the slider up or down. However, if you change the axis limits, this may no longer be true. The initial range of values on the x and y axes are in the same ratio, so a graph of y = x will be at 45°,Īnd circles would be round, not squashed into ellipses. The aspect ratio (ratio of width to height) of the graph window is exactly 4:3. GFE will check to ensure that the lower value is at the bottom of the y axis or the left of the x-axis. To change them, simply edit them in place and press GRAPH or the Enter key again. If you enter a value that is off the graph, the cursor will not show,īut the values of the functions for that x value will be displayed correctly.Īt each end of the x and y axis is a box containing the end values. You can enter the x value for the cursor manually into the text box in the upper left.Īfter entering a value press "Graph" or the enter key. It shows the values of each function where the cursor intersects that function. If you click on "show cursor", a thin vertical line appears. If left unchecked, each function is shaded in a different color. This allows you to more easily see where complex functions overlap, since the more overlap there is, the darker the shading. If this is checked, the shaded areas for all three functions are all the same light gray. When plotting inequalities, the "monochrome shading" checkbox can be used. The area of the graph where y is greater than the function value is shaded. The function will be plotted as a line as usual. GFE can be used to plot inequalities by changing the relational operator in the pull-down menu to the left of the function. It is best to always enter the correct expression yourself. It will add two extra closing parentheses so they balance and evaluate it as 2+(sin(x)) Note: This may not always produce the desired result. When you press GRAPH or enter, it will automatically add enough closing parentheses to balance them. You may have meant it as one over 2sin(x). Since there are no parentheses, it is executed from left to right so it sees it as one half of sin(x). For example if you enter 1/2sin(x) GFE inserts a multiply between the 2 and the sin. It will not work if the function is preceded by a variable name. For exampleģcos(2.1) will be automatically treated as if you entered 3*cos(2.1): three times the cosine of 2.1. If a function (such as sin() ) is preceded by a number, GFE assumes you want to multiply them. See PI definition for more.įor example you could enter sin(pi) or e^2.1 There are two constants you can refer to. Returns the smallest integer greater than or equal to x Returns the highest integer less than or equal to x Returns x rounded off to the nearest whole number Returns the absolute value of x (always positive or zero) The power to which you must raise e to get x.Į (approx 2.718) raised to the power of x. The power to which you must raise the 10 to get x. The trigonometry cotangent function, x in radians. The trigonometry cosecant function, x in radians. The trigonometry secant function, x in radians. The trigonometry tangent function, x in radians. The trigonometry cosine function, x in radians. The trigonometry sine function, x in radians. The function names are not case sensitive.Īll trigonometric functions operate in radians. GFE has the following built-in functions.

[mugggle-studies-blog]

USTET: A Guide

Subtests: Mental Ability, Math, Science, English

The USTET is one of the very first entrance test exams I ever took. It is also, in my opinion, among the easiest. The key to acing it? Mastering your high school classes. 

Or at least, passing all of them and acquiring enough stock knowledge. 

MENTAL ABILITY If I remember correctly, this subtest has 80 items and you have 25 minutes to answer it (don’t hold me on this, I’m not sure, but just know that the time is short and the subtest is long). The questions are easy, but they’re tricky. Make sure you read them correctly! It’s mostly logic questions and some basic math, if you’d call it that. A weird example I remember: “If I have 5 apples and give 2 to my friend, how many does my friend have?” My most important tip for this is to answer as many as you can. They’re going to tell you it’s okay not to finish it, but you should still aim to. Your scores on this subtest will matter.

MATH wELP, as you can probably tell from the results, math isn’t my strongest suit. However, I found the USTET’s math part relatively easy. It would definitely easier for people who are good in it or enjoy it. The most memorable part was the trigonometry questions because I couldn’t remember any of them. So know your trigo ratios! Values of the six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0∘, 30∘, 45∘, 60∘ and 90∘ appeared, so make sure you know those. As well as your high school Algebra and basic Geometry, of course.

SCIENCE The USTET’s Science part dealt with basic concepts. Questions focused mostly on recurring high school science concepts like erosion, plate tectonics, basic anatomy, etc. There wasn’t a lot of physics iirc, and those that appeared simply involved Newton’s Laws. Hopefully, you paid attention in your high school classes. 

ENGLISH Scour your pile of notes for those Oral Communication lectures because they’re basically the main content of this subtest. That’s all I have to say for this. 

TL;DR Answer the Mental Ability part quickly and efficiently, master high school Algebra, know your basic concepts in Science, and study your Oral Comm lessons.  Lastly, know the opposite of love. 

University of Santo Tomas website: http://www.ust.edu.ph/

[soapybitch]

Dave’s Short Trig Course

Angle in unit circle showing trig functions as lengths of line segments

Table of Contents

Who should take this course?

Trigonometry for you

Your background

How to learn trigonometry

Applications of trigonometry

Astronomy and geography

Engineering and physics

Mathematics and its applications

What is trigonometry?

Trigonometry as computational geometry

Angle measurement and tables

angle theta in a circle of radius r

Background on geometry

The Pythagorean theorem

An explanation of the Pythagorean theorem

Similar triangles

Angle measurement

The concept of angle

Radians and arc length

Exercises, hints, and answers

About digits of accuracy

Chords

What is a chord?

Trigonometry began with chords

sin is opp over hyp

Sines

The relation between sines and chords

The word “sine”

Sines and right triangles

The standard notation for a right triangle

Exercises, hints, and answers

cos is adj over hyp

Cosines

Definition of cosine

Right triangles and cosines

The Pythagorean identity for sines and cosines

Sines and cosines for special common angles

Exercises, hints, and answers

tan is opp over adj

Tangents and slope

The definition of the tangent

Tangent in terms of sine and cosine

Tangents and right triangles

Slopes of lines

Angles of elevation and depression

Common angles again

Exercises, hints, and answers

The trigonometry of right triangles

Solving right triangles

Inverse trig functions: arcsine, arccosine, and arctangent

The other three trigonometric functions: cotangent, secant, and cosecant

Exercises, hints, and answers

Pythagorean triples

graph of sin x

The trigonometric functions and their inverses

Arbitrary angles and the unit circle

Sines and cosines of arbitrary angles

Properties of sines and cosines that follow from the definition

Graphs of sine and cosine functions

Graphs of tangent and cotangent functions

Graphs of secant and cosecant functions

Computing trigonometric functions

Before computers: tables

After computers: power series

law of cosines

The trigonometry of oblique triangles

Solving oblique triangles

The law of cosines

The law of sines

Exercises, hints, and answers

law of sines

Demonstrations of the laws of sines and cosines

For the law of sines

For the law of cosines

Area of a triangle

Area in terms of two sides and the included angle

ptolemy's theorem

Ptolemy’s sum and difference formulas

Ptolemy’s theorem

The sum formula for sines

The other sum and difference formulas

Summary of trigonometric formulas

Formulas for arcs and sectors of circles

Formulas for right triangles

Formulas for oblique triangles

Formulas for areas of triangles

Summary of trigonometric identities

More important identities

Less important identities

Truly obscure identities

About the Java applet.

Images in Dave’s Short Trig Course are illustrated with a Java applet. If your browser is Java-enabled, you can drag the points around in the diagrams and the diagram will adjust itself. The applet also allows you to lift a diagram off the web page into its own floating window. For details, see About the applet.

Note that some web browsers do not allow printers to print images created by Java applets. You may still be able to print the images if turn off Java in your browser, and the plain images should appear that can be printed.

Select topic

Dave’s Short Trig Course is located

at http://www.clarku.edu/~djoyce/trig

[professionalcrammer]

MATH

- so okay im not supposed to be giving you advice in maths because I SUCK IN MATH. But i’ve fallen down and have risen!!! I got an average of 1.5 (our grading system here is different, 1 is the highest and 5 is the lowest!!!) in my last 2 math subjects so beat that!! ok here it is. btw, these r incomplete bcoz i haven’t finished those subjects yet (like geometry and physics but i’ll /try/ to give u accurate and nice tips) 

general tips

tip #1: if your professor permits you use your calculator, then make sure to always bring it!! 

tip #2: write down all your formulas every!!  single time!! there’s no harm in memorizing them right?? through writing them down, you’ll be familiar with the formulas and work your way through the problem easily!! 

tip # 3: practice. makes. perfect!!!!! can’t stress this e n o u g h! do not limit yourself with your textbook. the internet has a loooooooot of resources. use them wisely!! here is my fave website for free worksheets: Kuta Software

tip #4: convince urself that u love math omg!! hahaha be patient with the subject.if you’re having a hard time, IT’S OKAAAAAY!!!!!!!!!!!!!!! if i can do it we can all do it!! 

tip #5: math isn’t only math.... ?? ok u use it in every subject!! especially in chemistry!! i swear, don’t forget ur lessons!! 

tip #6: take good notes. it will help in the long run! 

tip #7: keep all your quizzes and papers!! 

tip #8: do not sleep in class and pay ATTENTION!! one wrong step will kill u. i promise. been there done that HAHA

tip #9: KNOW HOW TO GRAAAPH AND DRAAW. doesn’t matter how icky ur parabola or sine curve is bUT AS LONG AS IT IS IN THE RIGHT VALUES THEN YOU’RE GOOD.

tip #10: ALWAYS HAVE A SCRATCH PAPER AT HAND OK

tip #11: DON’T PANIC DOOOON’T PANIC I REPEAAAT. brEATHE fam it’s gonna be O K. 

A) Statistics

tip #1: statistics is easy, JUST AS LONG AS U DON’T MESS EVERYTHING UP!!!!! you just need to FOCUS on inputing your data. one mistake and everything won’t be right. slowly, but sUuuuuuuUuURELY

tip #2: know the functions of ur calculator!!!! if u didn’t know about this, then NOW U KNOW!! read the manual of ur calculator or watch videos online. knowing the functions of ur calculator especially for statistics saves a lot of time. 

tip #3: always know ur symbols!! like what does delta E stand for...etc!! 

tip #4: always always know the definition of basic terms like for example: mean, median, mode, sample size, and what those are for.

B) Trigonometry

tip #1: write down all the trigonometric functions!! memorize em if u can

tip #2: SOH-CAH-TOA!!! Sine:Opposite over Hypotenuse - Cosine: Adjacent over Hypotenuse - Tangent: Opposite over Adjacent!! 

tip #3: if there’s sin cos tan, there’s also cosecant, secant, and cotangent!! it’s just the reciprocal of soh cah toa!! :)

tip #4: know the relationship between things!! 

C) Calculus

tip #1: hmm...calculus. basically, memorize the formulas!! Like for limits, you have to identify if the given is a limit or not and there are steps to that. it’s important to KNOW and MEMORIZE them!! 

tip #2: calculus relies HEAVILY on word problems. the tip in solving those word problems is to approach them in an organized manner. I usually solve it through

first, read the problem carefully 

second, dissect the problem. Find out what is given and what u are looking for. Write down the given

third, solve, solve, solve!! solve carefully based on your given

for ur final answer, write it with completely with units n all!! 

tip #3: calculus can be applied in real life so ya better put ur thinking caps on and ask urself “how would i do this” (if this makes sense HAHA) 

D) Algebra

tip #1: ur X can be annoying...but u also ask Y. (horrible i know) the key to algebra is to SOLVE FOR X!!! x is important so if given with two unknowns such as x and y, always try n use x as y... ya get? lemme show u. 

Find two numbers x,y. If y is three times greater than x and has a sum of 20. so... in here, u can use x instead of y... since x is x, and y is three times greater than x so.. 3x=y. and since both is equal to 20, you can equate it like this: 3x + x = 20. Now u can group the 2 x’s and arrive at ur answer!! 4x=20, x=20/4, x=5!!! 

tip #2: don’t forget the signs!! integers could be PESKY AF and one wrong move can make a huge difference so don’t forget the signs. 

tip #3: Review your basic math operations. this is basic so if this is basic, this would be ez for u

tip #4: organization is the key!! as always, solve in a systematic way. :) 

E) Physics (haven’t took this course yet so...here r tips i found here) 

tip #1: (these tips r mine but from high school physics) always, read the text!! 

tip #2: identify the missing quantities!! 

tip #3: KNOW UR CONVERSION FACTOOOORS!!! know the different and basic conversions!! 

F) Geometry

tip #1: look at all the angles. angles r very very important here! so remember, 30, 90, 60!! and don’t forget SOH CAH TOA as well ok? 

tip #2: memorize the theorems so that u can approach all ur problems with ease. 

tip #3: im sorry i haven’t taken this course (and won’t SO HERE’S A BUNCH OF GOOD TIPS 4 YA NOT WRITTEN BY ME!!) anotha one

i believe in u OK?? GO CRUSH UR MATH SUBJECTS!! 

ur professional crammer,  pattycake <3 

[darveshclasses]

Integration |Exercise 9.2|Question 3 Solution|Elements of Mathematics |

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[mathematicianadda]

$ \int_0^\frac{\pi}{2}\ln^n\left(\tan(x)\right)\:dx$

I'm currently working on a definite integral and am hoping to find alternative methods to evaluate. Here I will to address the integral: \begin{equation} I_n = \int_0^\frac{\pi}{2}\ln^n\left(\tan(x)\right)\:dx \end{equation} Where $n \in \mathbb{N}$. We first observe that when $n = 2k + 1$ ($k\in \mathbb{Z}, k \geq 0$) that, \begin{equation} I_{2k + 1} = \int_0^\frac{\pi}{2}\ln^{2k + 1}\left(\tan(x)\right)\:dx = 0 \end{equation} This can be easily shown by noticing that the integrand is odd over the region of integration about $x = \frac{\pi}{4}$. Thus, we need only resolve the cases when $n = 2k$, i.e. \begin{equation} I_{2k} = \int_0^\frac{\pi}{2}\ln^{2k}\left(\tan(x)\right)\:dx \end{equation} Here I have isolated two methods.

Method 1:

Let $u = \tan(x)$: \begin{equation} I_{2k} = \int_0^\infty\ln^{2k}\left(u\right) \cdot \frac{1}{u^2 + 1}\:du = \int_0^\infty \frac{\ln^{2k}\left(u\right)}{u^2 + 1}\:du \end{equation} We note that: \begin{equation} \ln^{2k}(u) = \frac{d^{2k}}{dy^{2k}}\big[u^y\big]_{y = 0} \end{equation} By Leibniz's Integral Rule: \begin{align} I_{2k} &= \int_0^\infty \frac{\frac{d^{2k}}{dy^{2k}}\big[u^y\big]_{y = 0}}{u^2 + 1}\:du = \frac{d^{2k}}{dy^{2k}} \left[ \int_0^\infty \frac{u^y}{u^2 + 1} \right]_{y = 0} \nonumber \\ &= \frac{d^{2k}}{dy^{2k}} \left[ \frac{1}{2}B\left(1 - \frac{y + 1}{2}, \frac{y + 1}{2} \right) \right]_{y = 0} =\frac{1}{2}\frac{d^{2k}}{dy^{2k}} \left[ \Gamma\left(1 - \frac{y + 1}{2}\right)\Gamma\left( \frac{y + 1}{2} \right) \right]_{y = 0} \nonumber \\ &=\frac{1}{2}\frac{d^{2k}}{dy^{2k}} \left[ \frac{\pi}{\sin\left(\pi\left(\frac{y + 1}{2}\right)\right)} \right]_{y = 0} = \frac{\pi}{2}\frac{d^{2k}}{dy^{2k}} \left[\operatorname{cosec}\left(\frac{\pi}{2}\left(y + 1\right)\right) \right]_{y = 0} \end{align}

Method 2:

We first observe that: \begin{align} \ln^{2k}\left(\tan(x)\right) &= \big[\ln\left(\sin(x)\right) - \ln\left(\cos(x)\right) \big]^{2k} \nonumber \\ &= \sum_{j = 0}^{2k} { 2k \choose j}(-1)^j \ln^j\left(\cos(x)\right)\ln^{2k - j}\left(\sin(x)\right) \end{align} By the linearity property of proper integrals we observe: \begin{align} I_{2k} &= \int_0^\frac{\pi}{2} \left[ \sum_{j = 0}^{2k} { 2k \choose j}(-1)^j \ln^j\left(\cos(x)\right)\ln^{2k - j}\left(\sin(x)\right) \right]\:dx \nonumber \\ &= \sum_{j = 0}^{2k} { 2k \choose j}(-1)^j \int_0^\frac{\pi}{2} \ln^j\left(\cos(x)\right)\ln^{2k - j}\left(\sin(x)\right)\:dx \nonumber \\ & = \sum_{j = 0}^{2k} { 2k \choose j}(-1)^j F_{n,m}(0,0) \end{align} Where \begin{equation} F_{n,m}(a,b) = \int_0^\frac{\pi}{2} \ln^n\left(\cos(x)\right)\ln^{m}\left(\sin(x)\right)\:dx \end{equation} Utilising the same identity given before, this becomes: \begin{align} F_{n,m}(a,b) &= \int_0^\frac{\pi}{2} \frac{d^n}{da^n}\big[\sin^a(x) \big] \cdot \frac{d^m}{db^m}\big[\cos^b(x) \big]\big|\:dx \nonumber \\ &= \frac{\partial^{n + m}}{\partial a^n \partial b^m}\left[ \int_0^\frac{\pi}{2} \sin^a(x)\cos^b(x)\:dx\right] = \frac{\partial^{n + m}}{\partial a^n \partial b^m}\left[\frac{1}{2} B\left(\frac{a + 1}{2}, \frac{b + 1}{2} \right)\right] \nonumber \\ &= \frac{1}{2}\frac{\partial^{n + m}}{\partial a^n \partial b^m}\left[\frac{\Gamma\left(\frac{a + 1}{2}\right)\Gamma\left(\frac{b + 1}{2}\right)}{\Gamma\left(\frac{a + b}{2} + 1\right)}\right] \end{align} Thus, \begin{equation} I_{2k} = \sum_{j = 0}^{2k} { 2k \choose j}(-1)^j \frac{1}{2}\frac{\partial^{2k }}{\partial a^j \partial b^{2k - j}}\left[\frac{\Gamma\left(\frac{a + 1}{2}\right)\Gamma\left(\frac{b + 1}{2}\right)}{\Gamma\left(\frac{a + b}{2} + 1\right)}\right]_{(a,b) = (0,0)} \end{equation}

So, I'm curious, are there any other Real Based Methods to evaluate this definite integral?

from Hot Weekly Questions - Mathematics Stack Exchange from Blogger https://ift.tt/2keYK09

[er-cryptid]

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[tutoroot]

What are the Standard Angles of Trigonometric Table? 

The Trigonometric Table is essentially a tabular compilation of trigonometric values and ratio for various conventional angles such as 0°, 30°, 45°, 60°, and 90°, often with extra angles such as 180°, 270°, and 360° included. Due to the existence of patterns within trigonometric ratios and even between angles, it is simple to forecast the values of the trigonometry table and to use the table as a reference to compute trigonometric values for many other angles. The sine function, cosine function, tan function, cot function, sec function, and cosec function are trigonometric functions.

The trigonometric table is helpful in a variety of situations. It is required for navigating, research, and architecture. This table was widely utilized in the pre-digital age, even before pocket calculators were available. The table also aided in the creation of the earliest mechanical computing machines. The Fast Fourier Transform (FFT) algorithms are another notable application of trigonometric tables.

Standard Angles of Trigonometric Table

The values of trigonometric ratios for the angles 0°, 30°, 45°, 60°, and 90° are widely utilized to answer trigonometry issues. These values are related to measuring the lengths and angles of a right-angle triangle. Hence, the standard angles in trigonometry are 0°, 30°, 45°, 60°, and 90°. Following are the trigonometry angle tables (show the figure).

The trigonometric table in its simplest sense refers to the collection of values of trigonometric functions of various standard angles including 0°, 30°, 45°, 60°, and 90°, along with other angles such as 180°, 270°, and 360°. These angles are all included in the table. This makes it easier to determine and arrive at the values of the trigonometric ratios in a trigonometric table, also, the table can be used as a referral illustration to compute trigonometric values for various other angles, due to the patterns that are seen within the trigonometric ratios and those between angles.

The table as one might note, consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent. The short forms of these are very popular – sin, cos, tan, cosec, sec, and cot, respectively. Always, memorize the values of the trigonometric ratios of the standard angles.

Always remember these points in the trigonometric table:

In a trigonometric table, the trigonometric values for complementary angles, such as 30° and 60° are measured by applying complementary formulas for various trigonometric ratios.

The value for some ratios in a table is ∞ “not defined”. The reason is that while computing values, the denominator shows a “0”, which implies that the trigonometric value cannot be defined, and is as good to be the equivalent of infinity.

Please notice the sign change in the values at places under 180°, and 270°, for values of some trig ratios in a trigonometric table. This happens because there is a change in the quadrant.

Trigonometric values

As explained, if trigonometry deals with the relationship between the sides of a triangle (right-angled triangle) and its angles, then the trigonometric value refers to the values of different ratios, sine, cosine, tangent, secant, cotangent, and cosecant, all in the trigonometric table. All the trigonometric ratios are in relation with the sides of a right-angle triangle. The trigonometric values are derived applying these the ratios. Refer to the following steps to create trigonometric values:

Important Tricks to Remember Trigonometry Table

Knowing the trigonometry table can help you answer trigonometry problems and remembering the trigonometry table for normal angles ranging from 0° to 90° is simple. Knowing the trigonometric formulae makes remembering the trigonometry table much easier. The trigonometry formulae are required for the Trigonometry ratios table. These several trigonometry table techniques and formulae are explained below.  

sin (90°− θ) = cos θ 

cos (90°− θ) = sin θ 

tan (90°− θ) = cot θ 

cot (90°− θ) = tan θ 

cosec (90°− θ) = sec θ 

sec (90°− θ) = cosec θ 

1/sin θ = cosec θ 

1/cos θ = sec θ 

1/tan θ = cot θ 

Trigonometry values for trigonometry table – a summary

Three principal trigonometric ratios determine the trigonometric values: Sine, Cosine, and Tangent.

Sine or sin θ = Side opposite to θ / Hypotenuse

Cosines or cos θ = Adjacent side to θ / Hypotenuse

Tangent or tan θ = Side opposite to θ / Adjacent side to θ

The standard angles in a trigonometric table are: 0°, 30°, 45°, 60°, and 90°

The angle values of trigonometric functions, cotangent, secant, and cosecant are computed by applying these standard angle values of sine, cosecant, and tangent

All the higher angle values of trigonometric functions such as 120°, and 360°, are easier to compute, through the standard angle values in a trigonometric values table.

If you still can’t remember the values of Trigonometry tables, consider Tutoroot personalised sessions. Our online Maths Tuition session will help you understand the table and provide memorization tricks. 

[pandeprabhakar01-blog]

Corporate Secretarial Services Market Business Planning Research and Resources, Supply and Revenue 2018-2023

The report begins from overview of Industry Chain structure, and describes industry environment, then analyses market size and forecast of Corporate Secretarial Services by product, region and application, in addition, this report introduces market competition situation among the vendors and company profile, besides, market price analysis and value chain features are covered in this report.

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Corporate Secretarial Services assists clients to manage and mitigate risks of corporate non-compliance. Innovative techniques coupled with years of professional experience help ease administrative burdens across functional and geographical boundaries.

Company Coverage (Sales Revenue, Price, Gross Margin, Main Products etc.): Link Market Services, Adams & Adams, COGENCY GLOBAL, DP Information Network, UHY Hacker Young, Exceed, Company Bureau, RSM International, Dillon Eustace, PKF, French Duncan, Equiniti, Grant Thornton, Eversheds Sutherland, J&T Bank and Trust, BDO International, Conpak, EnterpriseBizpal, Rodl & Partner, A.1 Business, Luther Corporate Services, Elemental CoSec, MSP Secretaries, ECOVIS, KPMG, Mazars Group, Vistra, Deloitte, PwC and TMF Group.

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•        Food & Medical

•        Automotive

•        Electronics

•        Mechanical Engineering

Region Coverage (Regional Output, Demand & Forecast by Countries etc.):

•        North America

•        Europe

•        Asia-Pacific

•        South America

•        Middle East & Africa

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Table of Content

1 Industry Overview

2 Industry Environment

3 Corporate Secretarial Services Market by Type

4 Major Companies List

   4.1 TMF Group (Company Profile, Sales Data etc.)

   4.2 PwC (Company Profile, Sales Data etc.)

   4.3 Deloitte (Company Profile, Sales Data etc.)

   4.4 Vistra (Company Profile, Sales Data etc.)

   4.5 Mazars Group (Company Profile, Sales Data etc.)

   4.6 KPMG (Company Profile, Sales Data etc.)

   4.7 ECOVIS (Company Profile, Sales Data etc.)

   4.8 MSP Secretaries (Company Profile, Sales Data etc.)

   4.9 Elemental CoSec (Company Profile, Sales Data etc.)

   4.10 Luther Corporate Services (Company Profile, Sales Data etc.)

   4.11 A.1 Business (Company Profile, Sales Data etc.)

   4.12 Rodl & Partner (Company Profile, Sales Data etc.)

   4.13 EnterpriseBizpal (Company Profile, Sales Data etc.)

   4.14 Conpak (Company Profile, Sales Data etc.)

   4.15 BDO International (Company Profile, Sales Data etc.)

   4.16 J&T Bank and Trust (Company Profile, Sales Data etc.)

   4.17 Eversheds Sutherland (Company Profile, Sales Data etc.)

   4.18 Grant Thornton (Company Profile, Sales Data etc.)

   4.19 Equiniti (Company Profile, Sales Data etc.)

   4.20 French Duncan (Company Profile, Sales Data etc.)

   4.21 PKF (Company Profile, Sales Data etc.)

   4.22 Dillon Eustace (Company Profile, Sales Data etc.)

   4.23 RSM International (Company Profile, Sales Data etc.)

   4.24 Company Bureau (Company Profile, Sales Data etc.)

   4.25 Exceed (Company Profile, Sales Data etc.)

   4.26 UHY Hacker Young (Company Profile, Sales Data etc.)

   4.27 DP Information Network (Company Profile, Sales Data etc.)

   4.28 COGENCY GLOBAL (Company Profile, Sales Data etc.)

   4.29 Adams & Adams (Company Profile, Sales Data etc.)

   4.30 Link Market Services (Company Profile, Sales Data etc.)

5 Market Competition

6 Market Demand

7 Region Operation

8 Marketing & Price

9 Research Conclusion

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[rtirman-blog]

25.

That awkward moment in the upstairs hallway at the Holy Cross Central School of Nursing may appear to others as part of my experience with girls.  However, it was clearly an embarrassing work moment caused, and witnessed by, a nun! However, that X-rated comedy does bring to mind two persistent challenges in my life other than work and school i.e., making friends, and living with my Harriet, Wally, and my cousins.

 One of the first person’s I met was Bob Ernst. I can’t say that Bob and I ever did anything together, but I will never forget the day I met him. After getting a cup of coffee-to-go at the Huddle, I walked over to the La Fortune Student Center to relax.  I found a comfortable chair in the large ballroom as you enter the building.  It simply was a very comfortable, quiet, place with lots of comfortable chairs of the kind in which I was sitting.  I placed my books down on the coffee table, then picked up my newly purchased copy of Chaucer’s Canterbury Tales.  This was not a textbook, nor was it assigned reading.  I spotted this paperback copy at the Notre Dame Bookstore, and it reminded me of a night at Daddy’s when my brothers and I were visiting Phyllis and him in Brooklyn

 It was quite late, and we were discussing the Canterbury Tales.  Really, I ought to be saying that they were discussing the Canterbury Tales while I was on the couch trying so hard to stay awake.  I’d hear a bit of conversation or laughter and doze off, that would repeat and repeat itself for what seemed like all night.  But all of a sudden the laughter got real loud.  I awoke to see Daddy laughing so hard he was crying and giggling. I began to laugh. He took off his glasses, and tears were pouring down his cheeks. Why, in God’s earth was he laughing so uncontrollably? What was so funny?  The answer - one of the Canterbury Tales. To be precise it was The Miller’s Tale.  No one told me anything else, except that I should read it.  

 So, when I spotted the book in the book store, I snatched it up quickly; and then, in the quiet and friendly confines of the La Fortune Student Center, I read the Miller’s Tale.  Chaucer does not waste a single word!  Everything written is essential to the tale.  Once I reached the end of the story, I couldn’t believe how masterfully, and cleverly, every written word mattered.  Sitting there alone, I laughed and laughed. But I was not alone as I thought. A student, whom I did not know, sitting on the other side of the room, was laughing with me.  He made his way over to me, and wanted to know what I was reading that made me laugh so hard. He was laughing because I was laughing!  Just as everyone did for me, I told him what I read that made me laugh so hard, but I would not tell him anything more, so as to not spoil it for him. He and I became school friends through all my years at Notre Dame.  I don’t recall doing anything with him outside the University.  Actually, I had three other friends my freshman year, and I can’t remember doing anything outside the school. With any of them.  As I think back, all that makes a whole lot of sense.  Classes, labs, studying, and work at the hospital consumed most of my time….and energy!  But Alas! I still have not talked about life with my Aunt and Uncle and my cousins.

 My cousins were terrific. Whenever I had time to be around them, it was fun. But honestly, those times were few too many.  My Uncle Wally, who I loved dearly, somehow felt that I should show my appreciation by doing well in school and by doing chores, such as, trimming the ten-foot-high hedges, mowing and raking the lawn, shoveling snow, etc.  Occasionally, I watched the kids.  Another dimension to my stay with them was that Wally turned into a hovering parent. I grew up with practically no adult supervision, yet, I adjusted. Even though Wally had always had a great sense of humor, I found him to be a pretty stern person. However, I felt like I needed to do things his way.  He made a much better uncle than a parent.

I was hard to participate in anything at the University, and hard to develop friendships.  I hope it makes sense when I say I made three friends, and I have no idea how I met two of them – Tony Ciambelli and Ray Sayers. Ray was studying at Notre Dame with his eye on the Priesthood. I believe he was headed for the Congregation of Holy Cross (CSC) because most of the priests there were from that Order. In fact, Father Edward Sorin, the founder of the University, was a Holy Cross priest.

 (As an unimportant note of interest, up until this moment, I never put together Father Sorin and St. Edward’s Hall, in which I had the good fortune to live for a couple of semesters. I also just discovered that Father Sorin founded St. Edwards University in Austin, Texas.    One more aside -   It was pointed out to me, in a calculus class, how to remember the CSC after the names of Holy Cross priests.  As you may know, in a right triangle, the sine and cosecant are reciprocals. Therefore, csc=1/sin, or csc equals one over sin. Clever!)

 Tony was to become my roommate during my sophomore year. Besides wanting to live on my own, my Uncle thought it best that I leave.  He felt, I was a bad influence on my cousins.  Frankly, he either felt he put more on his plate than he could chew, or more likely, he feared that I might mess with Sari, who was mature beyond her 10 years. Just meeting that beautiful girl, you would swear she was eleven or twelve years old.  The only female that was ever in their house whom I would have liked the nerve to “attack” was Mary Lou Dillon. 

 Mary Lou was almost two years older than me.  She had to be the prettiest and nicest gal in the entire Midwest.  Mary Lou worked in my Uncles offices, and was the regular sitter for my cousins.  Just trying to talk with her was difficult.  I needed to gulp, but I didn’t want her to see me gulp, revealing my unrequited nerves. She was very friendly, and shared a huge secret with me. As most people didn’t know, on radio and aired to only Notre Dame students, there was a nighttime program called “Letters from Home” Since I was not on campus, I never heard Notre Dame’s rendition of “Tokyo Rose”.  Nonetheless, the boys (and that’s all there were at Notre Dame, boys!) would listen to the voice of a girl named Elaine.  At least, that’s what I think was her name. Mary Lou’s revelation to me was that she was Elaine!   All those guys drooling while listening to Elaine with her girl-from-home voice, read those breath-taking letters, and I was the Notre Dame student who knew her best- Mary Lou and I had a “secret”, or from my point of view a “secret relationship”.

 (I realize I jump from topic to topic. When I am writing about one thing, another thing comes into my mind. So I start writing about it.  Some people would advise me to simply jot down the new thought on another piece of paper. But I am not very organized, and I’ll lose that paper, for sure. Also, when and if I find that paper, I can’t be sure it would conjure up the thoughts I presently have in my mind. Sometimes, I think I have ADHD!)

 Back to Tony. Near the end of my freshman year, Tony said, for next year, he was going to rent an upstairs suite in a private home on the west side of South Bend.  He asked me to be his roommate.  After visiting with the Mr. and Mrs. Komp, the owners of the home, and after viewing the upstairs rooms, I agreed to rent the suite with Tony. We became roommates during my sophomore year.  However, I can’t recall actually doing anything with Tony or Ray during that freshman year.  I know we had lots of conversations, but I don’t remember whether we were on campus or off campus.  I’m certain, they would say I was their friend.  During finals in May, Tony, Ray, and I were finally getting together to go to the movies.  Due to a familiar circumstance, that get-together never happened.

 I need to back up to Father Lane and my first semester chemistry performance.  You might recall that I started off that class with a bang.  I was teaching other students the Periodic Table.  But just like many other things that I start off with a bang, my energy and interest waned, and I lost whatever enthusiasm I had for chemistry.  I really think I had too much time between classes, and my penchant for not showing up to my chemistry class went into high gear. My chemistry grades declined rapidly, while my pool skills improved slightly.  The end result?  I failed Chemistry with a 65 average, and that isn’t a final exam score!   So that meant I had to retake Chemistry.  The only course available during the Spring semester was being taught by Mr. McCusker, in the Engineering School. Obsessed with the same thoughts I had about taking Trigonometry twice in high school, I was over anxious to not do lousy the second time around. So I used my Uncle’s sure fire method of study.  Before a lecture, I read the chapter as if I was reading a novel. I did not to worry about remembering a thing that I read. I then would attend the chemistry class and took notes during the lecture. As immediately after the lecture as was possible, I corrected my notes using my chemistry book.  My notes were always in pencil for easy correction. Then, before the next chemistry class, I memorized those notes. Then, each day I went back to the first day of notes and reviewed all of them, from that first day to through the last entry.  In essence, that is a continuous recall of the notes from day one. I kept that up the entire semester.  I got a 100 % on every exam and every quiz, except the last quiz before the final.  I missed a question about an ice-salt mixture falling below 0 degrees Centigrade. Since I had the highest average in the class, and since I missed that question, I was right to expect that same question to show up on the final…it did!

 I was seen as a real bright student.  I tried to see myself in the same way, but my vision was tarnish by having failed the course before.  Anyway, the night before the final, I had told Wally that I had to study for the Chemistry final.  He, Harriett and the kids were off to an outdoor movie.  After they left, I got cleaned up, and went out the front door to be on my way to see Tony and Ray. However, just as I was walking away from the door, pulling up into the driveway was Wally, with wife and children. He had forgotten something, and came back to the house to get it. Today, I think he came back to get me. He asked me what I was doing. I told him I was going to go downtown to go to the movies with Tony and Ray.  He said, no! If you are not going to study for that chemistry final, then you will go to the movies with us.

 That’s exactly what occurred. I did not study for the final.  I did not go out with Tony and Ray. I went to an outdoor movie with the family. Wally was certain I would learn my lesson.  Well, I got a 100% on the final and a 97% for the course.  The student closest to me got a course grade of 91%…I guess I learned my lesson well!

[teesturtle]

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Making Sense Of The September TREB Numbers

TorontoRealtyBlog

I think a lot of you have been waiting for this; both the numbers, and my response to them.

The short of it is: the bears were wrong…..for one month, at least.

The long of it is: time could prove the bears right….because nobody knows what lays ahead.

Let’s look at September’s key real estate metrics, and I’ll share some of my own experiences from the past month, trying to navigate the difficult Toronto real estate market…

Sometimes, that’s how I feel when trying to make sense of the TREB numbers; like Matt Damon in front of a blackboard, attempting to solve a complex math problem.

I actually have no idea what the heck those symbols are.  They look like asterisks to me.  Actually, they look quite a lot like a map of airport terminals.

I think it’s been about 15 years since I had to find a derivative, or anti-derivative.

And it’s definitely been 20 years since I drew a parabola, or knew what sine, cosine, and tangent were.

Secant, cosecant, and cotangent?

My brother did a 5-year Hons. B.Math at the University of Waterloo, and I remember the textbook for one of his courses was twenty pages thick.  Twenty pages.  For an entire year.  I guess you’d spend an entire week trying to solve one problem.

There are no Fibonacci sequences in the September TREB numbers, which you can read at length HERE.

But there are a few statistics that make little sense, or that only confuse where we are in the market.

Recall my “Predictions For The Fall Market” blog post from September, which spawned a TRB-record, 202 comments.

I made one bold prediction, that I stuck to even as contrarians fumed: that the average sale price in September would be higher than that of August.

And honestly, how in the world is that to be considered “bold?”

As I said in September’s post, “This is a no-brainer.”

The average sale price couldn’t possibly dip from the $732,292 low that resulted in August.  It would have been impossible, in my mind.

Having dropped from over $920,000 in April, it just didn’t seem reasonable, in my mind, that we would see a fifth straight monthly decline in the average sale price, especially when you consider that, a) August is slow, b) September is busy.

The average sale price in September, in fact, increased by 5.6%, from August.

Recall that I took a lot of flak from people for that “Predictions” post after Labour Day, with comments like these:

No, this isn’t an “I told you so” moment, but rather I wanted to highlight another ongoing theme in this current real estate market, one that is gaining serious momentum: anger.

Read any newspaper article online in the Globe & Mail, National Post, or Toronto Star.  Any columnist who has the audacity to write a positive article about real estate gets absolutely eviscerated by the commenters.

Why are people so angry about real estate?

I have a theory, as you know.  And it’s one that a lot of you won’t like.

It’s that most market bears do not own real estate.

The folks championing this 30-40% market decline?  Most aren’t home-owners, I’ll tell you that.

The ones attacking newspaper columnists online, and hating anybody who has anything to do with real estate?  They don’t go home to their $2,000,000 detached in Playter Estates at night, I’ll tell you that too.

I suppose you could argue the opposite – that I sell real estate for a living, and I’ll continue to argue that the market is healthy, and will trend upwards, even though I’ve reiterated many times that I will sell real estate in markets up, down, and sideways.

But I’m not vicious.  The online comments for real estate news articles are downright nasty!  Why are people so mad about the direction of the real estate market, and why are they so spiteful and malicious at anything shining a positive light?

In any event, there are three key numbers I’d like to examine from this past month’s TREB numbers.

While we could look at a host of different statistics, these are the ones I find the most interesting:

1) Average Sale Price, Toronto 2) Average Sale Price, Condominium, 416 3) New Listings, Toronto

Let’s start with the one that gets the most attention…

–

  1) Average Sale Price

As previously noted, the average sale price increased 5.6% from August to September, which I really don’t find surprising at all.

I think a lot of us realized that the August figure was artificially low, partially because it’s the second-slowest month of the year, outside December, and partially because the ratio of condos to houses increased dramatically as the spring went on (you can read more about this in my September 11th post – “Making Sense of the Drop In Average Home Price”)

Let’s see where things stand, compared to my post in September:

The 5.6% increase stops a 4-month trend in a declining average sale price.

And the decline from April to September is now less pronounced at -15.77%, whereas this number had reached -20.5% in August.

The average home price is now back up over January’s level, however the big question in my mind remains: where does it go from here?

Look at the fall of 2016 for a moment.

We saw a 6.0% increase from August to September, which is exactly in line with this year’s 5.6% increase – yet another reason why I figured the average home price increasing in September was a no-brainer.

But after that big jump, we saw only a 0.9% increase in October, and then a 1.8% increase in November, before the yearly drop-off in December – a whopping 6.3%.

It bears mentioning here, just to get sidetracked if for only a moment, that a December drop-off is normal.  That doesn’t mean your home is worth 6.3% less in December than it was in November, but rather there are very few, if any, luxury homes sold in December, and the ratio of condo sales to home sales increased dramatically.

So back to the question at hand – what do we expect for October and November?

As I predicted after Labour Day, I do expect the average home price to increase 10% this fall, which would bring it back up over $800,000.

Not quite the same “no-brainer” as the average home price increasing from August to September, but I do think it’s going to happen.

We need only see the average home price increase another 3.1% to get to $800,000, and I think that could happen in October alone, let alone by the end of November.

–

2) Average Sale Price – 416 Condominium

Raise your hand if you haven’t heard at least once this past month, something to the extent of, “The condo market is holding steady.”

Had I made any sort of prediction in the past few months that the housing market would outpace the condominium market, as it always does, and should, I would have been dead wrong.

Another one of my bold predictions from the past was, “Fifty years from now, only the city’s elite will own freehold properties.”

I still stand by that prediction.

Simply put, there will never be any more freehold properties built.  Maybe tearing down a bungalow on a wide lot, and building two semi-detached homes on its place gives you another one home.  But as a percentage increase, specifically in the central core, we’ll be trending pretty close to 0.00% from here on out.

About 99% of “new” housing in the core will be in the form of condominiums.

And it doesn’t take Good Will Hunting to do the math, and see how the supply-and-demand equation will affect house values.

Having said all that, the numbers for the condo market are shocking.

Let me show you the average sale price for condominiums, specifically in the 416, and compare the monthly increase/decrease to that of the overall average sale price:

As you can see, the condominium market has been far less volatile.

But the decrease has also been far less pronounced.

The December-to-April increase in average sale price was 23.9%, in line with the 26.05% we saw in the overall average sale price in Toronto.

But the decline of the latter was 15.77%, as shown in the first chart, compared to a much smaller 4.19% decline in the average 416 condo sale.

Who would have ever predicted that the condo market would outpace the housing market in 2017?

What I’m seeing out there in the condo market right now is shocking.

Not to name names, but I showed a unit to investors on the weekend – east-side, 495 square feet, original 2004 finishes, priced at $399,900.  That’s already $808/sqft, with no parking, and no locker.

But wait – there’s a hold-back on offers, and the listing agent told me on Saturday night, “I might be getting a bully offer, or two, tomorrow.”

So what does that mean?  $425,000?  $450,000?

Are we really going to see a 2004-condition condo, no parking, no locker, break $900/sqft?

Whether it “only” gets $808/sqft, or whether it breaks $900, the activity is just insane.

And it can all be traced back to the lack of product available on the market, which, of course, the TREB numbers do not show…

–

3) “Increase” In Listings

This is where things get really interesting.

It’s also where many people, bullish or bearish, can be seen to “make numbers say anything they want.”

The September TREB number show:

New Listings +42.9% from August New Listings +9.4% from September, 2016

Active Listings +15.8% from August Active Listings +69.0% from September 2016

So first of all, what’s an active listing, and what’s a new listing?

“New Listings” are exactly as you would assume – a count of all the new listings that month in TREB, including those for properties that have already been listed, regardless of month.  The “New” listings does not sort, filter, or clean the data – it’s just all new listings.

“Active Listings” refers to the number of listings on the market on the last day of the month.

And to this day, nobody can really figure out why or when one is higher than the other.  Except Good Will Hunting, but he won’t tell us the secret…

I’ve always preferred to look at the “New Listings,” and while I know double-counting properties that have been listed more than once is the drawback, I find my buyer clients don’t care about an active listing that’s been on the market for 92 days; they seek new listings that hit MLS, which we need to see right away.

So the TREB numbers show massive spikes in listing, across the board.  There are four “+” symbols above.

New listings are up 42.9% since August, which is an insane increase.  But August is slow.  It’s the second-slowest month of the year, behind December, in the minds of real estate agents (ie. the number of sales, listings, et al, notwithstanding).

New listings are up 9.4% from September of last year, which I find encouraging, since prices increased 6.0% in September of 2016, and the more listings we see, in theory, the lower the prices should be.

So where does the confusion set in?  I mean, other than trying to understand how and why the “active listings” data is so far from “new listings,” and the increases have seemingly no correlation?

Well, if you were to ask any Realtor, “Are you seeing inventory out there?” the answer would be an emphatic, NO.

There’s no inventory, folks.

I don’t care what the numbers say.  There is just nothing to sell.

I know that sounds crazy, given the TREB numbers, but I don’t work in an “on paper” market, nor do I work in a theoretical one.  I work out there, in real market conditions, and whether I have a buyer looking for a house or condo, low-end or high-end, east or west, there’s just nothing to sell them.

I made fewer for buyer clients in September than in any month this year, and I have more buyers looking than any month this year.  Do that math.

And no, it’s not because the buyers aren’t looking, or are waiting for the crash – my buyer clients are ready to buy, today, if the right property comes out.  But we just aren’t getting the listings.

Let me show you last week’s listings from Wednesday and Thursday.

On every Realtor’s MLS home page, they can customize their “listings pane.”

Mine are broken down into the areas I find I work the most, which explains why you see the five groupings below.

Here’s a shot of Wednesday’s listings:

That’s right.  On Wednesday of last week, in C09, C10, and C11 combined, which is Rosedale, Moore Park, Leaside, Davisville Village, and parts of Yonge/Eg, there were only eight new listings, and that’s for both houses and condos.

Eight.

So let’s say that’s one house in Rosedale and Moore Park combined, one in Leaside, one in Davisville, then five condos at Yonge/Eg.

How many buyers are looking for houses in Leaside?  How many price points do they represent?  How does that one new listing for a house satisfy the market?

Here’s Thursday’s screen-grab:

From 28 “downtown” listings on Wednesday, to 49 on Thursday.

I’ve always told people that when the market is busy, you’re getting 60 per day.

When the market is really busy, you’re getting 80+.

When the market is crazy, you’re getting 100+.

And at certain peak times, on peak days, you can see 130-140.

So how in the world does 28, and 49, satisfy the market?

This is what I mean when I say, “There’s no inventory,” and yet we keep hearing about record inventory levels.

Let’s look at those inventory levels through the last year, and specifically look at the month-over-month increases, as well as year-over-year:

Again, if you look at the 42.9% increase in new listings month-over-month from August to September, it’s a big number.  But last month’s new listings only represented a 9.4% increase from the same level last year, which is a better comparison.

Seeing where inventory levels were in January and February certainly explains the run-up in prices.  You might argue the same for the 25,000+ listings in May.

But is 16,000 new listings “enough” to satisfy the market in a busy September?

And where are those new listings?

Why are we seeing such a dearth of new listings in the areas I track?  Why are my buyer-clients without options?

When I decided to title this blog “making sense of the September TREB numbers,” it was mainly in reference to your own interpretation, and as an unavoidable response, your predictions.

But it’s also in reference to actually making sense of numbers like the new listings, because what I’m seeing out there completely contradicts what I’m seeing on paper.

“No product” has been the theme this fall.

–

Now, I certainly don’t expect to see another 202 comments on this blog post, but I do expect to see a healthy debate.

What do you guys think?

Was September and aberration?  Will the new stress-test cut off the real estate market at the legs?

Do you think the October average sale price will be higher than September?

So many questions, so much to talk about.

And now you know why I left this blog for Tuesday…

The post Making Sense Of The September TREB Numbers appeared first on Toronto Real Estate Property Sales & Investments | Toronto Realty Blog by David Fleming.

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[tutoroot]

What are the Steps to Create Values for Trigonometry Table?

The Trigonometric Table is essentially a tabular compilation of trigonometric values and ratio for various conventional angles such as 0°, 30°, 45°, 60°, and 90°, often with extra angles such as 180°, 270°, and 360° included. Due to the existence of patterns within trigonometric ratios and even between angles, it is simple to forecast the values of the trigonometry table and to use the table as a reference to compute trigonometric values for many other angles. The sine function, cosine function, tan function, cot function, sec function, and cosec function are trigonometric functions.

The trigonometric table is helpful in a variety of situations. It is required for navigating, research, and architecture. This table was widely utilized in the pre-digital age, even before pocket calculators were available. The table also aided in the creation of the earliest mechanical computing machines. The Fast Fourier Transform (FFT) algorithms are another notable application of trigonometric tables.

Steps to Create Values for Trigonometry Table

Step 1: 

Make a table with the top row showing the angles such as 0°, 30°, 45°, 60°, and 90°, and the first column listing the trigonometric functions such as sin, cos, tan, cosec, sec, cot.  

Step 2: Determine the value of sin 

To find the sin values, divide 0, 1, 2, 3, 4 by 4 under the root, in that order. Consider the following example. 

Step 3: Determine the value of cos 

The cos-value is the inverse of the sin angle. To find the value of cos, divide by 4 in the opposite order as sin. For example, to find cos 0°, divide 4 by 4 under the root. 

Step 4: Determine the value of tan 

Tan is defined as sin divided by cos. Tan equals sin/cos. Divide the value of sin at 0° by the value of cos at 0° to get the value of tan at 0°. 

Step 5: Determine the value of cot 

The reciprocal of tan is the value of cot. Divide 1 by the value of tan at 0° to get the value of cot at 0°. As a result, the value will be as follows: cot 0° = 1/0 = Unlimited or Not Defined  

Step 6: Determine the value of cosec 

The reciprocal of sin at 0° is the value of cosec at 0°. 

cosec 0° = 1/0 = Unlimited or Undefined 

Step 7: Determine the value of sec 

Any common values of cos may be used to calculate sec. The value of sec on 0° is the inverse of the value of cos on 0°.

While we learn trigonometric values of the trigonometry table, it will also be interesting to take note of the application areas of the table. On a broader note, the trigonometric table is used in:

Science, technology, engineering, navigation, science and engineering. Before the advent of the digital era, the trigonometric table was very effective. In the course of time, the table helped in the conceptualization of mechanical computing devices. Trigonometric tables are also used in the Fast Fourier Transform (FFT) algorithms.

The angle values of trigonometric functions, cotangent, secant, and cosecant are computed by applying these standard angle values of sine, cosecant, tangent. All the higher angle values of trigonometric functions such as 120°, and 360°, are easier to compute, through the standard angle values in a trigonometric values table. If you still can’t remember the values of Trigonometry tables, consider Tutoroot personalised sessions. Our experts will help you clearly understand the table along with tricks to memorize. 

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