# Questions tagged [trigonometry]

Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles and other topics relating to measuring triangles.

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### For angles $A$ and $B$ in a triangle, is $\cos\frac B2-\cos \frac A2=\cos B-\cos A$ enough to conclude that $A=B$?

Brief enquiry: $$\cos\frac B2-\cos \frac A2=\cos B-\cos A$$ Optionally $$\sqrt\frac{1+\cos B}{2}-\cos B=\sqrt\frac{1+\cos A}{2}-\cos A$$ Is above equality sufficient to prove that it ...
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### Basic trigonometry + polygon geometry Where am I going wrong?

Question You are given a regular polygon with $2⋅n$ vertices (it's convex and has equal sides and equal angles) and all its sides have length $1$. Let's name it as $2n-gon$. Your task is to find the ...
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### Finding the hypotenuse of a triangle using angles and segment lengths. [closed]

In the diagram, $\angle CAB = 90^\circ.$ Let $D$ be a point on $\overline{AB},$ and let $E$ be a point on $\overline{AC},$ such that $AB = AC = DE,$ $BD = 9,$ and $CE = 8.$ Find $DE.$ [asy] unitsize(...
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### Calculating Velocity from Speed, X,Y Bearing, and Z Bearing

I'm not entirely sure how to go about it, but I have a data structure that gives me ...
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### How to calculate a point on the surface of a cone?

Consider a cone whose central line is located at $z=0$. We know the points on the upper and lower lines (red lines). Let's call them $x_1,y_1$ and $x_2,y_2$. How can we obtain the value of $z$ for ...
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### A doubt regarding proof of values of trigonometric functions at allied angles

There are certain identities that help us to determine the values of trigonometric functions at $\dfrac{\pi}{2}+x \text{, } \pi-x$ etc. given the values of $\sin x, \cos x$. Now, when we prove such ...
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### What is the proof for the factor formula? [duplicate]

This is known as the factor formula. It is used for the addition of sin functions. I don't understand how the two are equal though. How would you get to the right side of the equation using the left? ...
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### Drone camera view frustum

I am trying to derive formula (2) from here. Formula describes the size of an area seen from UAV camera: Length $W$ is given in the paper as $D\frac{\sin(α)}{cos(θ)cos(α)}$. Camera view $α$ is same ...
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### $\operatorname{tg}2x=-1$ find $x$ [closed]

$\operatorname{tg}2x=-1$ $x∈[\pi/2,\pi]$ I tried expressing $\operatorname{tg}2x=\sin2x/\cos2x$ but is there any elegant other method?
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### History of $\sin(nx) = 2^{n-1} \prod_{0}^{n-1} \sin\left(x + \frac{\pi k}{n}\right)$

What is the name of this identity? Who discovered this identity? What is the history behind this? I have looked up on Wikipedia with little documentation of the identity see finite product of ...
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### Is it possible to define trignometric functions over a finite field?

Is it possible to define trigonometric functions such as sine, cosine, etc modulo a prime p?
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### Trigonometric identity for $\cos^3 x \cos y$? [closed]

Is there any identity for $\cos^3x\cos y$? If $\cos x \cos y = \frac{1}{2}\left[cos(x-y)+\cos(x+y)\right]$, then how could I rewrite the this product as a sum?
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### Finding the $\lim \limits_{x \to 0} {1 - \cos(x)\over \sin(x) \ln(1+x)}$ using Taylor's series.

I am a bit stuck. This is what I have so far and I am not sure how to simplify it further: $${{x^2\over 2} - o(x^4)\over (x - {x^3 \over 6} + o(x^5))(x - {x^2 \over 2} +o(x^3))}$$ How do I proceed ...
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### Solve the equation $6\cos^4 y+\sin^2 y =5$

Solve the equation $$6\cos^4 y+\sin^2 y =5 \qquad (0\leq y \leq 360^\circ).$$ I used quadratics and got the answers $y= 18.0, 162.0, 198.0,$ and $342.0$ degrees, but it differs from the answer given ...
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### Using trigonometric functions for equation simplification

Assume I have a matrix $D$ whose its entries are as below : Where $A$ and $B$ can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? Or ...
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### How to figure out $\sin(1°)$? [closed]

Can $\sin(1°)$ be found manually so that I can know other measurements of sine without memorizing? As I am a student of class 8, please give the answer in a way that I can understand.
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### Range of arctan(x) in terms of anticlockwise angles [closed]

Why is the range of $\arctan (x)$ from $-\pi/2$ to $\pi/2$ ? It could be from $0$ to $\pi$ as well since $\pi/2<x<\pi$ gives the negative values of $\arctan(x)$ like $-\pi/2<x<0$.
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### If $\cos 17x = f(\cos x)$, then show that $\sin 17 x=f(\sin x)$

If $f$ denotes the function which gives $\cos(17x)$ in terms of $\cos x$, that is $\cos(17 x) = f (\cos x)$, then, prove that it is the same function $f$ which gives $\sin(17x)$ in terms of $\sin x$. ...
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### simple trigonometry solving and find the possible answers if [closed]

mpenter image description here here its a multi anser type question
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### If $C$ is the smallest angle of a triangle, SHOW $\sin(C/2)\leq 1/2$. What's the significance of $C$ being smallest?

Let $A$, $B$, and $C$ be the angles of a triangle, with angle $C$ as the smallest of them. Show that (i) $\sin \left(\frac{C}{2}\right) \leq \frac{1}{2}$ (ii) Hence, or otherwise, show that \$...
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### What are the best books for studying Algebra 1,Algebra 2,Geometry and trigonometry? [closed]

Background :ALgebra I.Non-eucledian geometry.And currently began trigonometry and ALgebra II. What the answer should be:Good Bokks on algebra I(elementary algebra),Algebra II(INTERMEdiate),Geometry ...