Mathematics Stack Exchange
Mathematics Stack Exchange

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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How prove this $\frac{\cos{x}-\sin{y}}{\sin{x}-\cos{y}}=\frac{1-2\cos{x}}{1-2\sin{x}}$

let $\dfrac{\pi}{2}
math110
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How do you simplify trigonometric functions?

How do you simplify trigonometric functions like $\tan(x)\sec(x)$ or $\csc(x)\cot(x)$ as well as other equations like $\frac{\tan(x)}{\sec(x)}$ and so on? And could you explain why you are doing the steps so I can understand it a little better and…
user135435
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Calculate the following expression

Calculate the value of $\sin a+\cos a$, knowing that $\sin a\cos a=0.48$ and $a$ belongs to $\left[\pi; \frac{3\pi}{2}\right]$? What I did is: $$\sin a \cos a=0.48\ \ |\times 2$$ $$\sin 2a=0.96$$ $a= \dfrac{\arcsin \frac{24}{25}}{2} + \pi n$ or…
wonderingdev
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Systems of polynomial equations

I have read an article in Wikipedia about solving of systems of polynomial equations, where for example if we consider equation using trigonometric function,we should change $\sin(x)$ and $\cos(x)$ with variables $s$ and $c$ and add new equation…
dato datuashvili
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Double Angle Formula?

I am just trying to figure out what formula I would use to solve this equation. The problem is solve $\cos(3\theta)=1/2$; for all $0\leq \theta\leq 360^\circ$. I want to say I would use the double angle formula but I am not positive.
rick
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Solve $7\sin^2(x) - 9\cos(2x) = 0$

I need to solve for x in the polynomial $$7\sin^2(x) - 9\cos(2x) = 0$$ I have tried approaching the problem in multiple ways. I am only looking for some hints, not the actual answer. Thanks :D
TwoShorts
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Finding inverse cosh

I am trying to find $\cosh^{-1}1$ I end up with something that looks like $e^y+e^{-y}=2x$. I followed the formula correctly so I believe that is correct up to this point. I then plug in $1$ for $x$ and I get $e^y+e^{-y}=2$ which, according to my…
user138246
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Precalc - Trig Identities

I only need a hint as to where to go from here. My problem is this: $$ \dfrac{1+\tan(x)}{\sin(x)}-\sec(x) $$ Here's my work trying to solve the problem, up until I got stuck. Did I make a mistake somewhere or make it more complicated than it should…
Tanner
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Speed of a bicycle wheel

OKAY I corrected a blunder and still have problems I'm following this diagram from my book: https://i.stack.imgur.com/urGXN.jpg It asks that if the chainring is 150 mm in diameter, the sprocket is 80 mm in diameter, and (from information from a…
Gᴇᴏᴍᴇᴛᴇʀ
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Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$

I need to show the steps to prove this identity: $$\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$$ I know that $\cos{2x}=\cos^2{x}-\sin^2{x}$. From there I do not know what to do. The solution should look like: $$\sin^4{x}=sin^4{x}$$ I need to prove…
user132551
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Proving Trig Identity

I'm trying to prove the following identity: $$\frac{\tan^2(x)+1}{\csc^2(x)} = \tan^2(x)$$ I tried this page but I couldn't make any sense out of their steps listed.
Tanner
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How to solve simple trigonometry equation.

So we are learning trigonometry in school and I would like to ask for a little help with these. I would really appreciate if somebody can explain me how I can solve such equations :) $\sin 3x \cdot \cos 3x = \sin 2x$ $2( 1 + \sin^6 x + \cos^6 x ) -…
Deepsy
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Finding $C$ if $ 3\sin A + 4\cos B = 6 $ and $ 3\cos A + 4\sin B = 1 $ in a triangle $ABC$

In a triangle $ABC$, it's given that the following two equations are satisfied: $$ 3\sin A + 4\cos B = 6 $$ $$ 3\cos A + 4\sin B = 1 $$ Source: ISI B-math UGA 2017 We have to find the angle $ C$. Now, it's easy to see that $ \sin C = 0.5 $ (by…
Parth Thakkar
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Trigonometric functions and formulas

Given that $\csc(\theta) = −\sqrt{2}$, $\tan{\theta} = 1$ and $−\pi < θ < \pi$, find the exact value of the angle $\theta$ in radians.
Alex
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Nice Arctan Identity

Prove that $ \text{arctan}\left(\frac{a+d}{c}\right)=2\text{arctan}\left(\frac{a}{c}\right) $ if $a, d, c$ are positive reals satisfying $$ a^4+a^2c^2+a^2d^2+2a^3d = c^2d^2 $$ (credit: bobthesmartypants)
user1380792
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