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Questions tagged [trigonometry]

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

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles.

Trigonometry is most simply associated with planar right-angle triangles. The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles.

One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles.

See Wikipedia's list of trigonometric identities.

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Is there a way to solve for $x$ in $\cos^{-1}(ax) / \cos^{-1}(bx) = c$?

Is there a way to solve for $x$ in $\dfrac{\cos^{-1}(ax)}{\cos^{-1}(bx)} = c$? I guess it comes down to, are there any sine multiplication formulas I don't know about? The motivation for this is to find $x_0$, $y_0$, $f$ and $a$ in the equation $y…
jnm2
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Cosine Trigonometry Question

Find the radian measure of $\theta$ if $0 \leq \theta \leq 2\pi$ and $$\cos(\theta)(2\cos(\theta)-1) = 0.$$ I'm very new to this topic, so what I did was to take the inverse of $\cos$ from both sides, and then you're left with $$2\cos(\theta) - 1 =…
John
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Trigonometric Identities HW

Learning trigonometry right now. I have a question that asks: Write the trigonometric expression in terms of sine and cosine, and then simplify: $$(\cot^2\theta + 1) \sin^2\theta$$ I know the answer is $1$. I'm confused on how to get there. I…
munchschair
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Evaluate $\tan\left(2\sin^{-1}\frac{\sqrt{5}}{5}\right)$ without using a calculator

Evaluate without using a calculator: $\displaystyle{\tan\left(2\sin^{-1}\left(\sqrt{5} \over 5\right)\right).}$ So I built my triangle hyp=$5$, adj=$2\sqrt{5}$, opp=$\sqrt{5}$. $$ \tan\left(2\theta\right) =…
Gᴇᴏᴍᴇᴛᴇʀ
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Trigonometrical equation

I have some problem with finding $\cos2x$ if $\cos^6x-\cos6x=1$ I replace the $\cos6x= \cos^23x-\sin^23x$ but I'am not sure it's a good way to figure it out.
Greor
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A relation between sine and cosine

I cannot figure out how this relation: $$\cos(\omega t)+ \frac{\zeta}{\sqrt{1-\zeta^2}}\sin(\omega t) $$ is equal to: $$\frac{1}{\sqrt{1-\zeta^2}}\sin\left(\omega t + \tan^{-1}\frac{\sqrt{1-\zeta^2}}{\zeta}\right)$$ I only found that this is not…
FdT
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solving $\frac{x}{3}+{[\frac{x}{3}]} = \sin(x) + [\sin(x)]$ for real x , in an efficient manner

$$\frac{x}{3}+{\left[\frac{x}{3}\right]}=\sin(x)+[\sin(x)]$$ I know the answer and the solution. $$-1 \le \sin(x) \le 1\Rightarrow-2\le\sin(x)+[\sin(x)]\le 2 \Rightarrow -2 \le \frac{x}{3}+\left[\frac{x}{3}\right] \le 2 $$ now there are different…
amatr
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Trignometry prove question

I am new to this website so Please forgive me for my mistakes. I have a question of trigonometry to prove and it is as (I dont know how to write theta symbol sorry for it) $(1-\sin \theta)/(1-\sec \theta) = 2\cot \theta(\cos \theta-…
Bhuvnesh Gupta
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If : $\tan^2\alpha \tan^2\beta +\tan^2\beta \tan^2\gamma + \tan^2\gamma \tan^2\alpha + 2\tan^2\alpha \tan^2\beta \tan^2\gamma =1\dots$

Problem : If $\tan^2\alpha \tan^2\beta +\tan^2\beta \tan^2\gamma + \tan^2\gamma \tan^2\alpha + 2\tan^2\alpha \tan^2\beta \tan^2\gamma =1$ Then find the value of $\sin^2\alpha + \sin^2\beta +\sin^2\gamma$ Please suggest how to proceed in such…
Sachin
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sum of perpendiculars of a regular 24 sided shape inscribed in a circle

The following question is from Gelfand and Saul's book 'Trigonometry' The question follows from a section about summing trigonometric series using a 'telescoping sum' method. I guess this is the method the authors intend. I apologise for the…
mikoyan
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trigonometric equation opening

Solve: $$ \sin x + \sin 3x + \sin 5x = 0 . $$ Attempt at a solution: applying formulas for summation of sine we get after a series of operations: $ \sin x(8 \cos x \cos 2x \cos x + 1) = 0$ equaling sine to $0$ we get one solution $180k$.…
Bak1139
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Trignonometry application

How do I solve this question? The angles of elevation of the top of a pole from three points A,B and C in a straight line(in the horizontal plane) through the foot of the pole are α, 2α and 3α respectively. If AB = a, then the height of the pole is…
Shaurya Gupta
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Solving trigonometry equation

Please help me understand how to solve this for $0\leq x\leq360 $ I seem to have a problem with equations with powers. $$3\sin^2 x-3\cos^2x+\cos x-1=0 $$ thinking that I would start by simplifying: $$3 (\sin^2 x- \cos^2x)+\cos x - 1=0 $$ How I…
Sylvester
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What is inverse tangent?

I recently started thinking about what inverse tangent is. It is obvious that the definition of tangent is $\frac{\sin x}{\cos x}$, however, what is inverse tangent? I first thought $\tan^{-1} x = \frac{\sin^{-1} x}{\cos^{-1} x}$, but it didn't seem…
Derek 朕會功夫
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$\sin (x)$ for $x\in \mathbb{R}$

My confusion is how do we define : $\sin (x)$ for $x\in \mathbb{R}$. I only know that $\sin(x)$ is defined for degrees and radians.. Suddenly, I have seen what is $\sin (2)$.. I have no idea how to interpret this when not much information is given…
user87543
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