Mathematics Stack Exchange
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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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Approximate range of sum of two trig functions.

Find the approximate range of the function y = 2 sin (6x) + sin (4x). My initial reasoning is that sin of anything maxes out at 1, so this function can be rewritten as y = 2 (1) + 1 The maximum of y is 3. Then I tried to refine my answer. If…
Marty B.
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Need Sine form of Cotangent equation

$$(b^2 - c^2)\cot A + (c^2 - a^2)\cot B + (a^2 -b^2)\cot C=0$$ I want this equation to be in the Sine form. Please help me with steps. Thanks a lot
Neel Bhasin
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Upon multiplying $\cos(20^\circ)\cos(40^\circ)\cos(80^\circ)$ by the sine of a certain angle, it gets reduced. What is that angle?

So if $P = \cos(20^\circ)\cos(40^\circ)\cos(80^\circ)$, I can multiply $P$ by $\sin(X)$ so that the entire expression reduces to something manageable. I then take the simplified product and divide it by $\sin(X)$ and should get the numerical value…
Kat
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Simplify using the Tangent Difference identity

I solved a problem to the point that I know the answer is $$\frac{2nr}{\tan\left( \frac{(n-2)\pi}{2n} \right)}$$ The question tells me that the answer is going to be $$2rn\tan\left(\frac{\pi}{n}\right)$$ Wolfram Alpha tells me the two are equal,…
Max
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Question on Trigeometry

I'm doing this question and I found out why a, b, and c can't be the answer. What about d, and e? I don't understand them. P.S the right answer is d :) Thank you very much.
user115667
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help me to show that $\frac{\tan(\alpha-\beta)+\tan\beta}{1-\tan(\alpha-\beta)\tan\beta}=\frac{m^2-n^2}{2mn}$

help me to solve this problem.How can I approach? If $\sin\alpha=\frac{m^2-n^2}{m^2+n^2}$ then show that $$\frac{\tan(\alpha-\beta)+\tan\beta}{1-\tan(\alpha-\beta)\tan\beta}=\frac{m^2-n^2}{2mn}$$
Fazla Rabbi Mashrur
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$\sum\cos=0$ and $\sum\sin=0$ when.......

help me to solve this problem. If $\cos(\beta-\gamma)+\cos(\gamma-\alpha)+\cos(\alpha-\beta)=-\frac{3}{2}$ then show that $\sum\cos=0$ and $\sum\sin=0$
Fazla Rabbi Mashrur
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Prove the following trigonometric identity.

$$\frac{\sin x - \cos x +1}{\sin x + \cos x -1}=\frac{\sin x +1}{\cos x}$$ I tried substituting $\sin^2x+\cos^2x = 1$ but I cannot solve it.
dona12
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General solutions of Trigonometric functions

Find the general solution of: $$\sin^3 \theta - \sin \theta = 0$$ Working out: (Factorise out) $$\sin \theta (\sin^2 \theta - 1) = 0$$ Solve for $\sin \theta$ and $\sin^2 \theta - 1$: For $\sin \theta = 0$ $$\sin \theta = 0$$ $$\therefore \theta =…
MATHSUSER
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Solving trigonometry identities by simplifying terms

Verify the identity by simplifying the left side. $\sin^2x-\sin^2y=\cos^2y-\cos^2x$
Mike
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Movement depending on angle value

I have an object and an angle value (clockwise) in my game. Depending on the angle, the object will move toward a certain direction. If the angle is 0, the object will move (0,1) per frame (x,y) where positive y is "up". If the angle is 90, the…
Saturn
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Is there a way to solve for $x$ in $\cos(ax)/\cos(bx)=c$?

Is there a way to solve for x in $\dfrac{\cos(ax)}{\cos(bx)} = c$? This is similar to the question on $\dfrac{\cos^{-1}(ax)}{\cos^{-1}(bx)} = c$.
jnm2
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How can I calculate $a$, $f$, $x_0$ and $y_0$ in $y = a \cos(f(x - x_0)) + y_0$ given four arbitrary points?

How can I calculate $a$, $f$, $x_0$ and $y_0$ in $y = a \cos(f(x - x_0)) + y_0$, given four arbitrary points $(x_1, y_1)$, $(x_2, y_2)$, … that the graph must go though? The complexity of substituting each $x_n$ for $x$ and $y_n$ for $y$, solving…
jnm2
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Maximum of |sin x| + |sin y| + |sin z|

If $x$, $y$ and $z$ are real numbers with the property $x+y+z= \pi$, then the maximum of $\sin x+\sin y+\sin z$ is $3\sqrt{3}/2$. Now, if $x+y+z=0$ then is the maximum of $|\sin x| + |\sin y| + |\sin z|$ again $3\sqrt{3}/2$?
user85046
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solve trigonometric equation $\cos(2x) + \cos\left(x\right) -2 = 0$

Hi I can't figure out how to solve this equation: $$\cos\left(2x\right) + \cos\left(x\right) - 2 = 0$$ I think I'm supposed to rewrite $\cos\left(2x\right)$ into something else and then go from there. I tried a bunch of rewrites but nothing seems…
S4M1R
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