#trigonometric equations

[er-cryptid]

Patreon

[striderkiss]

i’m really super sorry for the lack of content lately, school has been rough :( i’ll be back and ready to stridercest soon, i prommy!!

[mephistopheles]

i spent a few months working with shakespeare’s globe in london, which is a reconstruction of a theatre built in 1599, which itself is a reconstruction of a theatre built in 1576. obviously this was before they had the ability to put microphones on actors, so one of the big questions scholars had was ‘how did people hear the play?’ turns out, as ppl discovered when they rebuilt the globe, the circular shape of the walls (combined with the springy oak-and-plaster they were made of) create a huge amplifying effect on all sounds emanating from the stage, meaning—even today—everyone can hear just fine. and i was like. why are you surprised by this. why are people shocked that humans of the past actually Knew What They Were Doing. why are people amazed that machu picchu is architecturally genius or surprised that the iliad is devastatingly powerful or stunned that ppl were solving sinusoidal trigonometric equations possibly as early as 350 CE. history is not one long linear march leading up to Today, The Zenith Of Everything & just bc somethings newer doesnt make it better & i am not smarter than the guy who wrote gilgamesh. actually this post is about people who were introduced to star trek by the flashy new stuff and then watched the original series and were, for some reason, shocked that so much of it was “actually good”

[hypertextdog]

feel free to elaborate as desired or to name any particular methods you worked with that were more or less effective for you

[nininikki]

some help — c. springer

content warnings: sfw! fluff, suggestive (allusions to sex), math, tired/horny drug dealer!connie

author’s note: save me hazel-eyed drug dealer…hazel-eyed drug dealer save me…😔

“are you gonna come to bed? like, at all?” you droned, letting the silky fabric of your robe droop off your shoulders and down to the crooks of your arms in half-exhaustion. “you’ve been counting that money for, like, two fuckin’ hours.”

your boyfriend, sat on your guys’ couch with a notepad in one hand and a wad of cash lazed haphazardly in the other, looked up from the seemingly trigonometric equations scrawled against the paper. the concentration that once burdened his brow softened at the sight of you, clad in lingerie that had been rendered almost useless by the amount of time he’d kept you waiting. “i know, i know. just a lotta numbers tonight.”

connie was usually an ace with numbers, something you came to realize (and greatly appreciate) when he’d actually completed an unfinished page of your trigonometry homework after you’d fallen asleep amid the eleventh question. “would a fresh set of eyes help?” you asked, heading for a spot on the couch, but connie’s legs immediately parted to make space for you on his lap.

the pretty hazel tone of his eyes fogged with tiredness, and all it took was a, “shittt, i mean, you can try.” before you were plopping onto his lap and retracting his mechanical pencil from behind his ear.

“okay, okay. let me see…” you murmured, “forty percent of ten thousand four hundred and twenty-two…” avoiding a math-induced headache, you skimmed over the calculation he did to find the percentage and skipped right down to the part covered in hastily scrawled question marks: ten thousand four hundred and twenty-two minus four thousand one hundred and sixty-eight.

it didn’t seem to be anything more than simple subtraction, and for a moment you thought he was pulling your leg, but a quick glance over to his visibly stumped face told you the complete opposite. “see, the paper says four thousand one-twenty, but i counted one-forty.”

upon further examination, which only took about five seconds, the root of connie’s issue seemed to be staring right in your face. “babe, you forgot to carry your one.”

his frown deepened, and then relaxed in understanding. “…oh,”

you felt his arm snuggle you closer into his body, and with that, makeshift contentment running through his chest in the form of a low grunt. “you know what you need?”

at the feeling of your acrylic nails gliding down the nape of his neck, his eyes off the notepad and onto you for a refreshing five seconds. “what?”

“some help.”

“help?” your face, contorted with puzzlement, morphed into one of playful realization when connie’s fingertips breached the hem of your robe.

“yeah,” connie softly groaned, punctuating it with a kiss to the corner of your lips. “gettin’ up outta this.”

[kes-geiszler]

I think the more I look into trigonometry, the more time I spend with the identities, the more beautiful it becomes. It's all tangibly connected, you can see how they morph into one another and yet they're all unique. Trigonometric identities and equations are like the night sky to me, they are so varied and beautiful and yet so similar. They're all stars, with what seems to be a similar composition to one another, yet the amounts in which they're composed makes them individuals, and makes them special.

[shankhachil]

Countdown to JEE (Main): Week 4/33

This week's been a bit stressful because of unit tests and also because I haven't been very well, what with the weather change :') I did my best though!!

Test results:

Allen monthly test: 205/360, rank 2/8. In my defence, the questions were really hard and there were a few chapters I hadn't studied yet....

Topics covered:

Physics: Electrostatics; Electric Potential and Capacitance; Simple Harmonic Motion; Fluids; Modern Physics (5/3)

Chemistry: Alcohols, Phenols and Ethers; Halogen Derivatives; Isomerism; Ionic Equilibrium (4/3)

Mathematics: Matrices; Vectors; Differential Equations; Permutation and Combination (4/3)

Questions solved:

Physics: - Physics tuition question bank, Electrostatics and Electric Potential and Capacitance — 123 questions, 114 correct - Allen Electrostatics module, S — 28 questions, 25 correct - Physics tuition Potential and Capacitance module — 38 questions, 35 correct - Physics tuition Electrostatics module — 31 questions, 27 correct - Allen Student Question Bank, Simple Harmonic Motion — 40 questions, 32 correct - Allen Student Question Bank, Fluids — 20 questions, 20 correct Total: 280/60 questions, 253 correct

Chemistry: - Allen Organic RACE 1,2,3,4,5 — 50 questions, 43 correct - Allen Physical RACE 11, 12, 13, 14 — 40 questions, 34 correct - FIITJEE Alcohols, Phenols and Ethers module, Exercises 1, 2, 3, 4, 5 and 6 — 48 questions, 42 correct - Kota Question Bank, Halogen Derivatives, single-choice, multiple-choice, comprehension and matching-type — 162 questions, 138 correct - Kota Question Bank, Alcohols, Ethers and Epoxy, single-choice — 70 questions, 55 correct - Kota Question Bank, Isomerism, single-choice questions — 51 questions, 42 correct Total: 421/60 questions, 354 correct

Mathematics: - Cengage Algebra Matrices, multiple-correct questions — 33 questions, 26 correct - Allen Differential Equations module, O3 and O4 — 20 questions, 16 correct - FIITJEE JEE (Advanced) archives, Permutation and Combination — 31 questions, 26 correct - Yellow Book, Permutation and Combination, single-choice — 26 questions, 24 correct Total: 110/60 questions, 92 correct

GRAND TOTAL: 811/400 questions, 699 correct

I!!!! Still!!!! Need to work on my accuracy!!! it's so frustrating but I promise I am Trying My Best

Upcoming tests:

28/06 (Friday) — Test at physics tuition center (JEE (Advanced) pattern). Topics: Motion in One and Two Dimensions; Units and Dimensions; Electrostatics; Potential and Capacitance; General Organic Chemistry; Halogen Derivatives; Chemical Thermodynamics and Thermochemistry; Alcohols, Phenols, and Ethers.

30/06 (Sunday) — Online test for mathematics tuition (JEE (Advanced) pattern). Topics: Trigonometry; Logarithms; Quadratic Equations; Sequences and Series; Trigonometric Equations; Permutation and Combination; Functions; Limits, Continuity and Differentiability

See you again next week!

[etcetraetcetra]

•8.06.23, Thursday, P-8/30•

Today started as a very very veeeeery hot day. There was a constant gloomy cloud cover and I legit felt like I’d die if I don’t dip myself head to toe in water T_T. Around 12 noon, it started to thunder and we experienced a big refreshing storm. Anyway I was satisfactorily productive today. Although I need to study overtime to make up the lost course work, I am still glad I was able to study 7 hours today.

Things I did today-

Solved the Chemistry Magazine on Periodicity and Periodic Table

Read Redox Reaction from NCERT book.

Took down some missed class notes

Started doing Integration with Trigonometric equations involved in it.

Studied about 1/4th of Biological Classification.

[twilightxsun]

there's no calculus without "us"

You're struggling with your homework from the Calculus class you're taking at Macabria University. Raven, who loves math, takes it upon himself to tutor you.

some spoilers for chapter 30+

content warnings: kissing, sexual tension

rating: teen and up

word count: 1,540

ao3

For all the monsters you’ve slain and challenges you’ve overcome, you never considered that calculus might be your downfall.

It’s not that you’re bad at math—really, it’s not. You’re perfectly capable of understanding the concepts and performing the problems given to you. It’s just that there’s a learning curve, and sometimes the equations and theories seem like Greek to you.

“That’s because it is Greek,” Raven drawls. “Theta, sigma, alpha—and onward. You know that.”

“Obviously,” you reply, feeling a bit flushed as the admonishment. Taking classes at the local Macabrian university seemed like a great idea until you realized you have to manage your studies alongside the rest of the kingdom. It doesn’t matter that you’re Dracula’s designated heir; no legitimate professor will give you a slide on slipping grades, even if you did have to protect the town from an onslaught of rebel werewolves.

At least your Calculus II professor is understanding enough, and gives you extensions on the homework should there be a true emergency. That doesn’t excuse you completely, however, and so now you’re forced to spend the whole night at your desk catching up to meet the new deadline.

Thankfully, Raven is here to help. He caught you earlier in the library, peering over your shoulder to notice you struggling with integration by parts. At first he snarked at you, but then took a serious tone as he realized the severity of the situation. As much as he enjoys teasing and lording over you, he loves math even more—at wouldn’t shirk an opportunity to show off his skills to you, even if it does mean helping you pass your class.

You look down at your assignment. Only five more questions to go on this one, and then you’re moving on to trigonometric substitution. But that’s getting ahead of yourself—you’re still trying to understand how to integrate   multiplied by sin(x).

“Look, it’s simple,” he tries to explain. “The function only seems like you’ll endlessly integrate. There’s a trick to it. I’ll show you.”

You nod, and watch as he scribes on a piece of paper. You’ve been a little distracted by him; his lithe hands, the angular knuckles and long fingers. The sheen of his pale skin under your lamplight. How his eyelashes flutter when he looks down to concentrate on a question. You wonder how those hands might feel entwined in your own, or how they might trail down your body… the line of thought leaves you somewhat heated, and you force yourself to focus on what he’s doing. 

You watch him integrate the function once, but it leads to another integral.

“Hang on,” you say.

He looks up expectantly.

“I never remember what order to put the U, V, dV, and dU in,” you admit, “what is it again?”

Raven gives you an expression that’s a mixture of exasperation and barely concealed smugness. For a tutor, he’s exceedingly arrogant, and it would annoy you if he didn’t proceed to carefully explain what you’re confused by every time.

“Think of it like this,” he tells you. “UV light, minus voodoo. U times V, then subtract the integral V du. That’s how I remembered it.”

“UV light, minus voodoo,” you repeat. “I can remember that.”

“You’d better. Don’t you have an examination this week?”

“Yeah,” you sigh. “I’m not sure how I’ll do.”

His gaze sharpens on you, and he puts his pen down. He lifts his hand up to your chin, and turns your head to look straight at him. “You’ll do excellently,” he says confidently, “you have my help.”

You hold his gaze. “Are you expecting to take the credit if I pass?”

He laughs. “Considering that you’d never pass without me, I absolutely will.”

You pull back. “Never pass?” you say in mock outrage. “You have so little faith in me?”

“Fine,” he amends, “perhaps you’d barely pass.”

You roll your eyes. His fingers are still on your chin, and after a moment, his hand moves forward to caress your jaw. It’s an intimate gesture, and sends a spark of warmth through your body.

You want to lean into the feeling, but responsibility drags you back to the paper in front of you. Reluctantly, you pull out of his grasp and recenter your focus on your homework. 

If he looks disappointed, you don’t see it; your eyes are back on the problem. “You can continue your explanation.”

He’s quiet for a moment, then resumes as if nothing happened. “As I was saying, you integrate twice with integration by parts. First the whole function, then only the term with an integral sign. It produces two terms that don’t need to be integrated, and one integral matching the other side of the equation. Do you see?”

You nod.

“What do you think happens next?” he quizzes you.

Looking at the equation, you consider the possibilities. “Do you add the integral of e to the x times sin of x to the other side? That would give you two of them on the left…”

He looks pleasantly surprised. “That’s it—maybe there’s more hope for you than I thought. What then?”

You think about it. “If you divide by two, is the right side of the equation the final answer?”

He grins. “Well, look at that. You got it right. It seems you have been paying attention.”

You smile in return, gratified that you’re finally getting it. “I always pay attention to you,” you confess.

His eyes gleam in the dim light of your room. “Do you, now?”

Raven’s expression has gone from pleased to knowing. There’s a hungry glint in his eyes, and the look sends a shiver through you. You turn towards him, setting your assignments aside for now.

“Let’s take a break,” you suggest. “We’ve been working for hours.”

“Fine by me,” he says, “anything in mind?”

“Well,” you say, “I was thinking… I should thank you, somehow.”

He leans forwards, intrigued. Your knees knock together with his, and you keep them there. The contact is activating—drawing you closer. You find yourself near his face, and your gaze drifts to his lips. He does the same, lidded eyes glancing up and down before meeting your own.

Tension rises between you, taut like a bowstring. You observed him all evening, unable to deny the magnetism that draws you toward him. You know you’re not alone in the feeling; he’s been looking back at you. It’s why you make the final move, pressing forward to catch his lips in a sweet kiss.

It’s not the first, or the second; but it is the only time you’ve been completely alone together. True intimacy is difficult when you’re with a group, especially when Alexis was right there, watching you give into desire for somebody else. There’s a shred of guilt at the thought, but you push it away. They know you’ve never been one for exclusivity. Still, you know it hurt them when Raven dragged you in for a hard, claiming kiss in front of everyone; and again, when Alexis chose to appease Percy while you sat off to the side, indulging Raven.

You can’t help it. He’s a burning flame, and you’re the moth, unable to resist his dangerous light. You think you can taste the fire on his lips, as heat washes through you. The kiss starts slow, but quickly evolves into something more passionate. His touch taps open a dark want in you, riveting your senses like no one else can. 

It’s not like with Alexis, who’s been your steadiest and most loyal companion for years. Their love is leisurely and unchallenging; you’re pretty sure they scored 99% vanilla on the BDSM test, but they hid the results from you, so you’re only speculating.

Raven is wild; undulating rapids, the roaring whirlpool sucking you into dark, hidden depths. You crave that excitement, the all-consuming blaze. It’s a terrible want that only satiates when his lips press against yours, and you hate to admit it, but you’ve been pining in the weeks since your last encounter like this.

For minutes, you just kiss. You find yourself in his lap, thighs around his. Your fingers tangle in his hair, and his hands wrap around your waist, pulling you flush against his body. Teeth clash together and he sucks on your tongue, and you breathe heavily between kisses. You wish the heady feeling you’re overcome with would never end, but alas: the unfinished homework sitting on your desk calls out your name.

Regretfully, you break away. He looks dazed, pupils blown in his cobalt blue eyes; hair mussed, lips swollen from kissing—and some biting. Self-satisfied at his unkempt appearance, you smirk. He raises an eyebrow.

“Well,” he says, a little breathlessly, “that was unexpected.”

“Oh, come on,” you croon, “you didn’t think I was going to send you away without a reward?”

He smirks back. “The night’s still young, Lord Protector, and you’ve quite a bit more to do. Would I be right in assuming you’ll have a grander thank you later for me?”

You laugh lowly. “Mmm… maybe if you help me pass my exam.”

He laughs back. “Oh, trust me. You’re going to ace it.”

[falsettos-tight-knit-family]

Homework

Jason: Marvin!

Whizzer: What's up, Jason?

Jason: Hi, Whizzer. Can you tell Marvin to come down here? I need help with my homework.

Whizzer: Well I don't see why I couldn't help you with that. Marvin's not your only smart dad, you know. When I was your age, I did pretty well in school, if I do say so myself.

Jason: Then why didn't you go to college?

Whizzer: .. Not important. What subject do you need help with?

Jason: Pre-calculus. Usually I like this class, but we're working with trigonometric functions right now and it sucks *shows Whizzer a currently blank graph next to a complicated trig equation*

Whizzer:

Jason:

Whizzer: ... You know what, let's get Marvin down here-

[itssmerafecameron]

RAFEYYY HOW DO U DO TRIGONOMETRY PAPA SAID U DIDN'T KNOW HOW TO DO MATH BUT IM DOUBLE CHECKING

Hi sweetheart let me explain in steps yeah I hope this helps or right sweetheart.

1) Reduce the given trigonometric equation in terms of the basic trigonometric ratios.

2) Factorize the given trigonometric polynomial in terms of the ratio.

3) Solve each factor and write down the general solution.

[soapver4]

Slice-of-Life Hailstorms

Remake + 🐶-🔎🔍 Hybrid Idea: Two talented high school math teachers tremble and transform into Siberian Huskies whenever a hailstorm begins in their hail-prone town, which is how they meet, bicker and fall in love ("This four-legged one is better at math than me!" "My students don't have a smidge of that weird doggo's passion for math!" "Silly me. I thought s/he was the real deal."). To return to their human forms, the couple must solve a math problem perplexing anybody. In preparation for such emergencies, people familiar enough with them would keep some math books around or bookmark math websites. When the transformation happens too far away from those people, though, the couple needs to look for math victims and solve the problems surreptitiously without freaking out anyone.

By and by, however, the couple looks beyond the awkwardness, inconvenient hunger pangs, etc. to embrace the light-hearted side of their predicament, solving equations and scratching out polygons, nodes and edges together with their paws on the snow-like ground. Sometimes, they would straighten out an unknowing neighbor's grocery budget, etch out the answers on a flour-covered kitchen table and peek from the yard at the neighbor's spooked but enlightened expression. Sometimes, they would untangle an inventory mystery threatening a perplexed work couple's dinner date. Sometimes, it's optimizing a delivery person's route. Sometimes, they would compete with each other to calculate the areas of quirky features of their town to fight for the right to a rare dog biscuit, occasionally uncovering land development corruption scandals in the process. Sometimes, they would revisit the simple joy of apple and orange story problems. Sometimes, they would trace out wild trigonometric curves and circles on the hills and pull each other on makeshift sleds along the resulting paths.

The world is still volatile and suffering. But in their two-canine microcosm, at least, math is not a hated symbol of stress, a cold KPI or a mere stepping stone for uncaring administrators' and learners' careeristic advancements.

[pissmd]

But in the course of the leap and the dive, my overlong arm hit the heavy iron pole of the high-intensity standing lamp that stood next to the bed. The lamp teetered violently and began to fall over sideways, away from the bed. It fell with a kind of majestic slowness, resembling a felled tree. As the lamp fell, its heavy iron pole struck the brass knob on the door to my closet, shearing the knob off completely. The round knob and half its interior hex bolt fell off and hit my room’s wooden floor with a loud noise and began then to roll around in a remarkable way, the sheared end of the hex bolt stationary and the round knob, rolling on its circumference, circling it in a spherical orbit, describing two perfectly circular motions on two distinct axes, a non-Euclidian figure on a planar surface, i.e., a cycloid on a sphere:

The closest conventional analogue I could derive for this figure was a cycloid, L’Hôpital’s solution to Bernoulli’s famous Brachistochrone Problem, the curve traced by a fixed point on the circumference of a circle rolling along a continuous plane. But since here, on the bedroom’s floor, a circle was rolling around what was itself the circumference of a circle, the cycloid’s standard parametric equations were no longer apposite, those equations’ trigonometric expressions here becoming themselves first-order differential equations.

Because of the lack of resistance or friction against the bare floor, the knob rolled this way for a long time as I watched over the edge of the comforter and mattress, holding my glasses in place, completely distracted from the minor-D shriek of the vacuum below. It occurred to me that the movement of the amputated knob perfectly schematized what it would look like for someone to try to turn somersaults with one hand nailed to the floor. This was how I first became interested in the possibilities of annulation.

— David Foster Wallace, Infinite Jest

[kayatoastkkat]

rating my topics tested for maths exam next week!

algebraic fractions and formulae: 7/10 actually not bad, need to watch out for the careless mistakes tho

direct and inverse proportion: 4/10 not that familiar with it

congruence and similarity: 4/10 its…not bad

pythagoras' theorem: 7/10 how hard can an equation be? (i will be proven wrong)

trigonometric ratios: 0/10 i cried and received trauma

[zozo-333]

Not sure if I'm actually going to write that but, potential spoiler I guess

(H-bombs ticking AU, although it can apply to others scenarios too)

Wouldn't it be funny like in 'I Triple Dog Dare You', everyone's dare were all like wicked, crazy dangerous stuff that might kill you. And Heather or Harold(not sure who's going to be there) just like, make you do math? Or let you answer a question with the most important part being coded?

Like 'Solve this trigonometric equation under five minutes', or 'repeat π to (Morse Code) decimal point'