I found a print of a trigonometric functions graph from 1937.
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can someone explain the six trigonometric functions?

i have a test in a few hours and i dont understand shit

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I found a print of a trigonometric functions graph from 1937
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Why are trigonometric functions ratios?

I am currently studying precalculus at school but we have already finished the part dedicated to trigonometry. I have understood how the functions work, what they look like and how they behave, but I feel that I have a big piece of it missing.

I have studied for example that the sinus is the ratio between the opposite catet and the hypothenuse, but both Google and my teacher could not explain me why this is true.

Maybe I am asking a stupid question, but I would love to understand why and how this works, why does this magical ratio return a value that has then such an important role in analytics.

The same thing is true for the cosine, tangent and cotnagent. I think this would help people better understand trigonometry and why and how it works, including me.

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I found a print of a trigonometric functions graph, originally drawn in 1937.

This is the coolest thing I've ever found at an antique store. I've never been able to find any information on either the guy that drew this, who was a "natural resources pictographer" named R.A. Brooke, or this graph. He filed for patents in USA and Canada in 1937 but my Google Fu is terrible. I've also never seen another functions graph like this, or even found any information on this one. Anyone got anything? I'm incredibly curious.

Edit: fixed my link

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Help me understand this trigonometric function

If sin(πœƒ) = 2/3, what is sin((pi/2) - πœƒ)? There are two answers.

The two answers are (sqrt(5))/2, -(sqrt(5))/2. How do I get there? Does it have something to do with sin being an odd function?

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Trigonometric functions formulas

https://preview.redd.it/nmib61osajk61.jpg?width=720&format=pjpg&auto=webp&s=2752ff614d3da318aba3409ce3afc07e9a747b53

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The 6 Trigonometric Functions are there meaning

Can someone please explain what the 6 Trig Functions are and how they are used. I understand how to find them but I struggle to see them as more than random values.

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Trigonometric functions grade 12

I don't understand how to solve these... something isn't making sense to me. If someone could break it down step-by-step even more so than they have with the 'feedback' I would appreciate the help

https://preview.redd.it/rr0jhfmn9xh61.png?width=850&format=png&auto=webp&s=fec028dbe396ee781647b8e57a95ad98199c0f1e

https://preview.redd.it/goaakcpm9xh61.png?width=862&format=png&auto=webp&s=011b78029f40b0399b5c56d601d2286f5def53a2

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πŸ“…︎ Feb 16 2021
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[Gymnasium ("high school")] What do the trigonometric functions represent? They just seem like illogical magic buttons on the calculator.

Press button angle go brrrrr and shit. Put the wrong number and they don't even work. What the hell do they represent!? Do they even have a value? How come arctan can magically produce two different numbers (radians and degrees)?

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finding the value of trigonometric functions

I'm really struggling on this questions:

sin(-13Ο€/6) = -1/2

csc 5Ο€ = undefined

tan (-16Ο€/3) = -√3

I have the answer sheet but I'm struggling on how to use the triangles and unit circle to figure this out. Any help is greatly appreciated!

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πŸ“…︎ Feb 10 2021
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Need a little help with a trigonometric function

So I got f(x)=x^2-sin(2x) with -pi/2<x<0 (also equal but I don't know how to add it here), and the question is to find where the slope is at its max and where its at its min.

I know the derivative is f'(x)=2x-2cos2x and that it can give me the max and min slopes of the original f(x) if I equal it to zero, but then I get:

cos2x=x, Which I don't how to get an answer from, help?

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[Linear Algebra] Basis of a subspace spanned by Trigonometric functions.

So I have this question, and I'm clueless on how to approach it, I'm getting that B is linearly dependent hence it can't be a basis anyway.... If I could be given some direction, I'd be grateful

V is a subspace that is spanned by the functions f , g :R->R which are defined by:

g(x) = CosX and f(x) = SinX.

We'll also define the functions h, k:R->R by:

h(x) = 2sinX+cosX and k(x) = 3cosX

Prove that the groups B = {f,g} and C = {h,k} are basis for V.

So when I tried solving this I thought to myself, well ok let's look at B first, it's told that V is spanned by f,g so the Span{B}=V, I just need to prove that B is Linearly independent and it's a basis!

So B is linearly independent if for the two scalars a,b: a*f(x)+b*g(y)= 0 only and only if a=b=0

But f(0) = sin0 = 0 and g(pi/2) = cos(pi/2) = 0

So a*f(0)+b*g(pi/2)=0 for any a,b.....

I'm clearly doing something wrong here, I'm not sure how to approach this.

EDIT: Even for the same x for g(x) and f(x) there's a solution in which a,b are not 0 scalars

proof, https://he.symbolab.com/solver/step-by-step/1%5Ccdot%20cos%5Cleft(%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi%20n%5Cright)%2B%5Cleft(-1%5Cright)%5Ccdot%20sin%5Cleft(%5Cfrac%7B%5Cpi%20%7D%7B4%7D%2B%5Cpi%20%20n%5Cright)

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[IB Maths AI SL: Trigonometric Function: General Sine functions] I'm stuck on the question C, how do I figure out the value for theta if the graph only provides such a limited number of values.
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(Grade 11 Trigonometric Functions) need help with this question
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Expansion of Trigonometric Functions in Partial Fractions

Hi r/learnmath!

I'm a grad student in Electrical Engineering. Part of my work is related to implementation of weird functions as electrical components. The issue is: electrical components can only represent sums of partial fractions, and we have a lot of theorems for that (i.e. Foster Theorem).

So, in order to apply my knowledge in electronics engineering, I need knowledge in math first. How can I represent trigonometric functions as a sum of partial fractions? I don't need an answer here, just for someone to point me to the right place.

I've been looking at the Laurent series because I remembered it from my Complex Analysis course, but I don't think it suits the problem.

Thank you so much for the attention.

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[Grade 12 Math: Solving trigonometric Functions] I dont understand why my answer is wrong and how to get to the right answer. Can someone explain please?
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Relation between Hyperbolic and Trigonometric Functions

Hey! Calc 1 student here. As I understand it both are essentially the same but on a different shape. Trigs for Unit Circle and Hyperbolics for Unit Hyperbola. My question is that Hyperbolic functions have an equation like sinhx = (e^x - e^-x)/2 but what about Trigonometric functions? Do they have an equation like this one or is it all calculated geometrically?

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Calculus 2: Trigonometric Substitution with arc trig Functions

I've never posted in this sub before so I don't know if I did the title right. I've been able to do trig sub before but that was usually only with one dx. I don't know how to integrate the indefinite integral when I substitute the trig terms. I know the final answer comes to 1.571 but the first time I tried I got -5, I don't know how to get to 1.571 and can't find any examples online with 2 dx's.

https://preview.redd.it/bqcdds0h2z261.png?width=1152&format=png&auto=webp&s=1cb5b1ad637cad2f7e6f8bef8d440df4ae865437

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Teacher: trigonometric functions are not that difficult to understand. The Trigonometric functions:
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Inverse trigonometric functions and trigonometric equations

INVERSE TRIGONOMETRIC FUNCTIONS AND TRIGONOMETRIC EQUATIONS

Solve for all real numbers x or angles with degree measure ΞΈ satisfying the equation and the indicated condition.

  1. 6sin²x + 7sinx - 5 = 0, x ∈ [0°, 360°)

  2. 2cos² x + 3cos x + 1 = 0, x ∈ [0°, 360°)

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Problem with Maple (symbolic algebra software) and trigonometric functions

Hi there fellow numberphiles.

I have been doing some calculations in Maple but face the following issue:

&gt;> sin(2.x)

I am pretty sure it mess up with my calculations, although it does not mention an error.

Any help would be greatly appreciated.

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[Trigonometric Functions]I hereby summon the chamber of Einstein’s ,to help me solve this.
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Korean pre-sat math problem (about trigonometric function) (2021.9)

I tried to translate this problem into English perfectly, but it's quite hard for me because of my poor English skills (: Hope you solve the problem well!

-----------------

Q. Let f(x) and g(x) be

f(x)=sin(k*x)+2, g(x) = 3cos(12*x)

defined on a closed interval [-2*pi, 2*pi]. Find the number of k which satisfies the following.

------

If real number a is y-coordinate of an intersection point between two curves y=f(x) and y=g(x), then {x/f(x)=a} βŠ‚ {x/g(x)=a}

-------

The answer is '4'.

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True Indology: "Modern trigonometry comes from India. Trigonometric functions Sine and Cosine originate from Sanskritic Jyā & kotijyā. These functions were used in Sūrya Siddhānta hundreds of years BEFORE Islαm. The outdated book you are quoting was written by a convert! SIT DOWN and learn!
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Infinite function composition of trigonometric functions

So I was just wondering and playing around with a graphing calculator online (desmos.com) and when inputting cos(sin(x)), the graph sort of looked like the graph of sin(x) or cos(x) but squished, I repeated the function composition cos(sin(cos(sin(...)))) and the range of the function kept getting tighter nearly looking like a constant function. I know why this happens - the range of sin(x) is 0 <= sin(x) <= 1, the range of cos(a) for some a 0 <= a <= 1 is 0.55... <= cos(a) <= 1, and so on and so forth, so it sort of squeezes the entire graph each time. I calculated 100 of these repeated function compositions using Python and the value was approximately 0.786... I'm wondering, is there an exact value for this and what is this as the number of function compositions goes to infinity, and if so, how one would calculate similar function compositions.

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πŸ“…︎ Nov 29 2020
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Building intuition around trigonometric functions?

Hello!

I'm currently working through Calculus (self-study. Came to math a bit late and discovered that I love itβ€”just wish I had started younger), and I'm finding most of it intuitive and lovely. I consistently, however, get a little confused around problems involving trigonometric functions.

The course I'm working through provides many "rules" around the various trigonometric functions, but I've found that while other rules of calculus are fairly intuitive once I've worked with them a bit, the trigonometric functions always feel like raw memorization. My brain isn't very good at that kind of operation (pulling from pure recall). If I look at a calculus problem that's concerned with some operation I haven't done in weeks, I can generally solve it by working from a simpler place and "rediscovering" the rule for solving it, if that makes sense. With trig functions, I simply can't. If I don't remember the rule for taking the derivative of csc or whatever, I have no choice but to look it up.

Does anyone have any suggestions for how I might build more of an effective mental model around trigonometric functions? I've done some trigonometry lessons over at Khan Academy, but a lot of it still felt like rote memorization and not mental modeling.

Any help would be greatly appreciated!

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