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.

29665 questions
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Please check my proof and let me know if incorrect.

$$\frac{1-\cos^2 x}{\tan x}= \sin(x)\cos(x)$$ i did the following working on LHS: $$\frac{\sin^2 x}{\tan x}=\frac{\sin(x)\sin(x)}{\tan x}=\sin(x)\cos(x)$$ i need to confirm that $$\frac{\sin x}{\tan x}=\cos(x)$$
user118512
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Why does this assumption change the formula this way

I am working through some notes and I cannot understand why the following assumption changes the formula as such. The formula is basically referring to a right angled triangle of base $ L $ and height $ \frac{D}{2} $. The difference between the…
user120625
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$\cos^2\frac{1}{2}(\alpha-\beta)=\frac{3}{4}$ if...........

Help please: If $\sin\alpha+\sin\beta= \sqrt{3} (\cos\beta-\cos\alpha)$ then show that $\cos^2\frac{1}{2}(\alpha-\beta)=\frac{3}{4}$ please tell…
Fazla Rabbi Mashrur
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Solving a linear trigonometric equation

Let $n$ be a natural number. For $a_i,\omega_i,\varphi_i \in \mathbb{R}$ how can one find solutions $x \in \mathbb{R}$ for the equation: $$\sum_{i=1}^n a_i \cos( \omega_i \cdot (x-\varphi_i)) = 0$$
Alex Gsiberger
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Prove Trig Identity

For any three angles $\alpha,\beta,\gamma$, show that $$\sin(\alpha-\beta)+\sin(\alpha-\gamma)+\sin(\beta-\gamma)=4\cos\frac{\alpha-\beta}2\sin\frac{\alpha-\gamma}2\cos\frac{\beta-\gamma}2$$ This is what I've…
user116528
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If $A + B + C = \pi$, then show that $\sin(A) + \sin(B) + \sin(C) = 4\cos\frac{A}{2}\cos\frac{B}{2}\cos\frac{C}{2}$

So i have $A + B + C = \pi$ $$\frac{A}{2} + \frac {B}{2} + \frac{C}{2} = \frac{\pi}{2}$$ $$4\cos\left(\frac{-B-C + \pi}{2}\right)\cos\left(\frac{-A -C + \pi}{2}\right)\cdots$$ And I doubt this leads to anywhere. So then I tried,…
Kat
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Find angle inside of isosceles triangle

The figure explains it best. We have $ABC$ isosceles triangle. We know a few angles as follows: $$\begin{align} ACB &= 20°\\ PAB &= 50°\\ ABQ &= 60° \end{align}$$ Find $\angle BQP$
Gabor Magyar
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Find a point n distance away from a specified point in a given direction

I'm waaay over my head here. Basically, I have a point (x, y) and a direction in degrees; I need to find a point that in n distance away from the given point in the specified direction. I've tried looking up similar issues but everything is beyond…
user1960364
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To show inverse of tan x

It quite confuses me. Where do I start? Please help.
Alexanderakk
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trigonometric system

In order to show that $ e^{ix}+e^{iy}+e^{iz}=0 \Longrightarrow e^{2ix}+e^{2iy}+e^{2iz}=0 $, I want to prove that $ \cos x+\cos y+\cos z=0 $ and $ \sin x+\sin y+\sin z=0 \Longrightarrow \cos 2x+\cos 2y+\cos 2z=0$ and $ \sin 2x+\sin 2y+\sin 2z=0 $ $…
Chon
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How do I calculate the phase shift between sine and cosine?

I know that $\sin(\alpha + x)=\cos(\alpha)$. How do I find $x$ ? I'd start by using the angle sum identity for sine: $\cos(\alpha)*\sin(x)+\sin(\alpha)*\cos(x)=\cos(\alpha)$ I had some ideas about what to do next but they didn't get me anywhere.
fgm2r
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$\sin(3x) = \sin(x)$

I know I'm supposed to do $\sin(3x) - \sin x = 0$ but beyond that I'm stuck.. I tried expanding $\sin(3x)$ but that didn't help. I want the value of $x$ in the interval $[0, 2\pi)$
andrei
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Why is $\sin(x) = \sin(180^{\circ}-x)$

I cannot seem to understand why this is true. Same for $\cos(x) = -\cos(180^{\circ}-x)$ and $\tan(x) = -\tan(180^{\circ}-x)$. Without the use of the compound angle formulas. Thanks
salman
  • 1,690
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Verifying trig identities

$$\sec(2x)=\frac{\sec^2x+\sec^4x}{2+\sec^2x-\sec^4x}$$ I have no idea how to verify this. I've tried changing it into cosine but it doesn't work.
user108452
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Arithmetic sequence of tangent values

I have two angles $A_1, A_2 > 0$, and $A_1+A_2 < \pi$, is it possible to find an $A_0$ such that $$\tan(A_0),\ \tan(A_0+A_1),\ \tan(A_0+A_1+A_2)$$ forms an arithmetic sequence on the same continuous range of tangent? I have been looking for a…
peterwhy
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