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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2D collision equations with inverse y-axis

I am currently trying to code a 2D physics engine in gamemaker studio, however I have run into a problem. I have found the following useful website to help me calculate the new x and y components of my speed vector after…
lygho
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Trigonometry pre calculus level good question

Here is a trigonometry problem. Given $$\frac{\cos(\alpha-3\theta)}{\cos^3(\theta)}=\frac{\sin(\alpha-3\theta)}{\sin^3(\theta)} = m$$ Show that $$m^2+m\cos(\alpha) = 2.$$ I tried to convert $\sin^3(x)$ into $\sin(3x)$ and similarly to…
Kamal
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Can $\sin(xy)$ be written in terms of trigonometric functions of only $x$ or $y$?

Can $\sin(xy)$ be written in terms of trigonometric functions of only $x$ or $y$? I am tempted to say yes, because the double- and half-angle formulae exist, and these would be special cases of $\sin(xy)$. I first looked at the Taylor…
gen-ℤ ready to perish
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Why should we have $\sin^2(x) = \frac{1-\cos(2x)}{2}$ knowing that $\sin^2(x) = 1 - \cos^2(x)$?

Why should we have $\sin^2(x) = \frac{1-\cos(2x)}{2}$ knowing that $\sin^2(x) = 1 - \cos^2(x)$? Logically, can you not subtract $\cos^2(x)$ to the other side from this Pythagorean identity $\sin^2(x)+\cos^2(x)=1?$ When I look up trig identities,…
Dylan O'Rear
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Are trig identities commutative?

If I have $\cos(B)\cos(A)-\sin(A)\sin(B)$, can I write that as $\cos(A)\cos(B)-\sin(A)\sin(B)$? And then combine it as $\cos(A+B)$?
A A
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Finding the general solution for trigonometric equation

Solve for general solutions $\tan(x/3) = 1$ When I solve this equation my answer comes to be $x = 3\pi/4 \pm 2n\pi, 15\pi/4 \pm 2n\pi$ where $n$ is an integer However when I graph the equation $y = \tan(x/3) - 1$ values for $x$ such as $11\pi/4$…
Ludwig
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What is the value of the expression $\sin\frac{2\pi}{7}\sin\frac{4\pi}{7}+\sin\frac{4\pi}{7}\sin\frac{8\pi}{7}+\sin\frac{8\pi}{7}\sin\frac{2\pi}{7}$?

This is rather a simple problem that I'm posting ; looking forward not for the solution of it but the different ways it could be solved. What is the value of…
Tanuj
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What is the value of the expression $[1 + \cos(\frac{\pi}{8})][1 + \cos(\frac{3\pi}{8})][1 + \cos(\frac{5\pi}{8})][1 + \cos(\frac{7\pi}{8})]$?

This is rather a simple problem that I'm posting ; looking forward not for the solution of it but the different ways it could be solved. What is the value of the following expression? $$\left( 1+\cos { \left( \frac { \pi }{ 8 } \right) } …
Tanuj
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Prove $\cos6x=32\cos^{6}x-48\cos^{4}x+18\cos^{2}x-1 $

So far I've done this: LHS $ =\cos^{2}3x-\sin^{2}3x$ $={(4\cos^{3}x-3\cos{x})}^2 -{(3\sin{x}-4\sin^{3}x)}^2$ $=16\cos^{6}x+9\cos^{2}x-24\cos^{4}x-9\sin^{2}x-16\sin^{6}x+24\sin^{4}x$ I can tell I'm going in the right direction but how should I…
Raknos13
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Keeping the change in angle constant

Say I have a ball under a plane that has been secured to the ground on the left, as shown in the diagram (the red part). When I push the ball to the left, the angle increases. If I wanted the change in angle to be constant, what velocity function…
thuy
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If $\frac{3-\tan^2\frac\pi7}{1-\tan^2\frac\pi7}=k\cos\frac\pi7$, find $k$

I need help solving this question: $$ \text{If }\frac{3-\tan^2\frac\pi7}{1-\tan^2\frac\pi7}=k\cos\frac\pi7\text{, find k.} $$ I simplified this down to: $$ \frac{4\cos^2\frac\pi7-1}{2\cos^2\frac\pi7-1} $$ But am unable to proceed further. The value…
Abhigyan
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Condition for three roots

The equation $$2\sin ^3 x +(2\lambda -3)\sin ^2 x -(3\lambda +2)\sin x -2\lambda=0$$ has excatly three roots in $(0,2\pi)$ then what can be the value of $\lambda$ . I thought for three roots the differentiation of the equation should have two roots…
Koolman
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$\alpha + \beta + \gamma = \pi$ , show that $\cos 2\alpha + \cos 2\beta + \cos 2\gamma + 2\cos\alpha \cos\beta \cos\gamma = 1$

$\cos 2\alpha + \cos 2\beta + \cos 2\gamma + 2\cos\alpha \cos\beta \cos\gamma = 1$ I really didn't know how to solve this problem and I am very unused to the utilization of trigonometric identities, I was wondering if I may have some assistance in…
John Rawls
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Problem relating to trigonometry

I was helping someone with her homework the other day, doing trigonometry problems. I ran into something which I wasn't too sure how to work out. The question was: Find every possible answer in terms of $\pi$. $$(\sin^2 x)+(\sin x)-2=0$$ I broke…
alex
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What would happen if you divide each side of the equation $\cot\beta\cos2\beta = 2\cot\beta$ by $\cot\beta$?

Explain what would happen if you divide each side of the equation $\cot\beta \cos2\beta = 2\cot\beta$ by $\cot\beta$. Is this a correct method to use when solving equations?
Ali Elcavs
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