# Tagged Questions

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

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### Find the value of x of $\frac{(3x^2-27)(8x^2)6}{4(9-3x)(x^2+3x)}=\frac{\tan (x+4)}{\log (x+\frac{1}{4})}$? [closed]

$\frac{(3x^2-27)(8x^2)6}{4(9-3x)(x^2+3x)}=\frac{\tan (x+4)}{\log (x+\frac{1}{4})}$? How to find the value of $x$ I've been thinking for this question for quite a time. Hope can somebody solve it. ...
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### How to solve this $80^\circ$-$80^\circ$-$20^\circ$ triangle ($60^\circ+20^\circ$ and $70^\circ+10^\circ$ variant)? [duplicate]

A friend of mine asked me for help with a math problem and I struggled with this for over an hour. I told him sorry, and I felt bad. It's been bugging me now for hours. I don't even so much care for ...
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### Why should the solutions of $(\sin x)^2 = 0$ be rejected in the equation $((\sin x)^2)(\csc x + 1) = 0$?

Q: Determine the number of solutions for $((\sin x)^2)(\csc x + 1) = 0$ over the interval $0 \leq x < 2\pi$ with the correct reasoning. Correct answer: There is one solution because the solutions ...
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### Is there a way to measure an angle, without using any protractor or trig finctions that requires a calculator? [closed]

Say i have an angle printed on a paper, Is there a way to measure it?
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### How to derive two angles and a length from this diagram [closed]

I'm familiar with sohcahtoa, the sin and cosine rule, I just can't seem to apply them here. I know angles alpha and ow, I know lengths z and al. I need to know length ? and angle ?? and angle Q
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### Inverse trigonometric function identity doubt: $\tan^{-1}x+\tan^{-1}y =-\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)$, when $x<0$, $y<0$, and $xy>1$

According to my book $$\tan^{-1}x+\tan^{-1}y =-\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)$$ when $x<0$, $y<0$, and $xy>1$. I can't understand one thing out here that when the above ...
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### $\tan x= \cot (x+\phi)$ for some $\phi$

Suppose we graphed the equation $y = \tan x$. Is it possible to describe this graph with an equation of the form $y = \cot (x + \phi)$, for some number $\phi$? Why or why not?
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### Small circles on sphere: finding angles for constant “cosine” onto a parallel.

My problem can be best explained starting from a 2D example: Imagine having a circle and wanting to discretize N points on the circumference of the circle so that the difference of the cosine of each ...
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### Is there a mathematical reason why rotation in the counterclockwise direction positive and clockwise rotation negative?

This inquiry has recently come to me in my study of trigonometry and the unit circle. It was said right from the very start that counterclockwise rotation were positive while clockwise rotations are ...
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### How are extracted this formulas from Tait-Bryan rotation matrix

I've a Tait-Bryan rotational matrix with this order X,Y,Z: Matrix Image I want to extract a Roll angle and Pitch angle from this matrix, and this are the two formulas: Matrix Equations Image I ...
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### how to get the angle of arc ??

dart game board is divided into sectors by 30 degrees like pizza slice. the given is (x, y) coordinates, and I need to find where coordinates are lying on. how can I get the angle just with ...
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### How to do this problem [closed]

Given: $$\sin(\theta')+\sin(\theta")+\sin(\theta''')=3$$ Find: $$\cos(\theta')+\cos(\theta")+\cos(\theta''')=?$$ How to solve this equation i tried to convert every term in terms of cos but it ...
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### Shortest route around a circle [closed]

Sorry I am very short of sleep so I hope this makes sense. I have a revolving stage which is programmed to move in a sort of linear fashion. One rotation of the revolve CW from a zero point would be ...
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### If the sides of a triangle satisfy $(a-c)(a+c)^2+bc(a+c)=ab^2$, and if one angle is $48^\circ$, then find the other angles.

In triangle $ABC$ one angle of which is $48^{\circ}$, length of the sides satisfy the equality: $$(a-c)(a+c)^2+bc(a+c)=ab^2$$ Find the value in degrees the other two angles of the triangle. I ...
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### Brocard Angles proof by Sine and cosine formulae.

The angles denoted by $\omega$ are the Brocard angles. Recently i came to know about the Brocard Angles and also their property i.e $\cot{\omega}=\cot{A}+\cot{B}+\cot{C}$. In my previous question I ...
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### What is the value of tan θ in this problem?

If $\vec{A} = 4\vec{i}+3\vec{j}$, $\vec{B} = 5\vec{i}-12\vec{j}$ and $\theta$ is the measure of the angle between the two vectors $\vec{A}$ and $\vec{B}$, then what is the value of $\tan \theta$?
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### Find the graph of the given function

$f(x)=$$Sin^{-1}$${(3x-4x^3)}$ , Plot the graph for $f(x)$ I want to know how I can plot graph from this points.
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### If $f(x) = \frac{\cos x + 5\cos 3x + \cos 5x}{\cos 6x + 6\cos4x + 15\cos2x + 10}$then..

If $f(x) = \frac{\cos x + 5\cos 3x + \cos 5x}{\cos 6x + 6\cos4x + 15\cos2x + 10}$ then find the value of $f(0) + f'(0) + f''(0)$. I tried differentiating the given. But it is getting too long and ...
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Let $n\in \mathbb{N} , n> 1$ Prove that : $\forall x\in (0,\frac{ \pi}{4(n-1)})$ $\tan(nx)> n \tan(x)$ I know: $f(x) = \tan x$ is convex function $f(a x + b y) < a f(x) + b f(y), a+b=... 2answers 51 views ### If$\sin(\pi \cos\theta) = \cos(\pi\sin\theta)$, then show … If$\sin(\pi\cos\theta) = \cos(\pi\sin\theta)$, then show that$\sin2\theta = \pm 3/4$. I can do it simply by equating$\pi - \pi\cos\theta$to$\pi\sin\theta$, but that would be technically wrong as ... 4answers 105 views ### Value of$\int\tan^{-1}(x)\,dx$What is the value of$\int^{1000}_{0}\tan^{-1}(x)\,\mathrm d x$? Today we were taught about graphs of all trigonometric inverse functions. So my proofessor split it into$0-\tan(1)$and$\tan(1)-...
If $xy + yz + zx = 1$, then show that $$\dfrac{x}{1-x^2} + \dfrac{y}{1-y^2} + \dfrac{z}{1-z^2} = \dfrac{4xyz}{(1-x^2)(1-y^2)(1-z^2)}$$ I tried doing the sum algebraically, that is, by solving ...
Consider the following integral, $$\mathrm{I} = \int_{-1}^{1}\frac{d}{dx}\tan^{-1}\left(\frac{1}{x}\right)dx$$ We can do this in two ways, First Using the fact that the antiderivative of \$\frac{d}{...