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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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Number of solutions of this trigonometric equation.

Q. Find the number of solutions of the equation $\sin(x) + 2\sin(2x) - \sin(3x) = 3$, in the interval $x\in (0,\pi)$. I tried clubbing the $\sin(x)$ and $\sin(3x)$ terms together but got nothing. I also tried the $\sin(x)$ with $\sin(2x)$ and…
Shaurya Gupta
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How to solve $x\left(\sin x+\cos x\right)=1$?

Could you please give me some hint how to solve this trigonometric equation: $$ x\left(\sin x+\cos x\right)=1$$ Since $\sin x+ \cos x= \sin x+ \sin\left(\frac {\pi}…
user97484
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how to solve equation with cos

I have this equation $\cos2x +5 \cos x + 3=0$. To solve it I rewrite $\cos2x$ to $2 \cos^{2} x- 1$ and set $\cos = t$. I get the following equation $2t^2 - 1 +5t +3 = 0$ with that and then divide the equation with two $t^2 +\frac{5}{2} t +1 = 0$. I…
S4M1R
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Finding the exact value of $\tan(\pi/5)$

Hi, I realise there has been a question already asked regarding this particular exact value, but this question requires for it to be done under different conditions, which is the part I require help in. I have been having trouble with this for the…
daleaf. M
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Simplifying a summation involving "cos".

$\sum_{r=1}^{n-1}\cos ^{2}\left ( \frac{r\pi }{n} \right )$ How can I simplify this summation when I do not know whether "n" is odd or even?
Niharika
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Question of trigonometry

If $\cos^2 A=\dfrac{a^2-1}{3}$ and $\tan^2\left(\dfrac{A}{2}\right)=\tan^{2/3} B$. Then find $\cos^{2/3}B+\sin^{2/3}B $. I tried componendo and dividendo to write the second statement as cos A but i couldnt simplify it
Himanshu Arora
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Losing information when solving trig problem

I was doing a simple trig question when it turned out I was missing several answers. I have read somewhere that it is possible to lose information about the signs when dealing with squares and square roots and wondered if something similar happened…
E.O.
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Simplifying trig expression

I was working through some trig exercises when I stumbled upon the following problem: Prove that: $ \cos(A+B) \cdot \cos(A-B)=\cos^2A- \sin^2B$. I started out by expanding it such that $$ \cos(A+B) \cdot \cos(A-B)=(\cos A \cos B-\sin A \sin B)…
E.O.
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Intuition around why domain of x of arcsine and arccosine is [-1;1] for "real result" & domain for arctangent is all real numbers

Context I'm working my way through basic trig (this question has a focus on inverse trig functions, specifically arcsine, arccosine and arctangent ), using Khan Academy, wikipedia and some of "trig without tears" -…
drc
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How to calculate the coordinates of the middle point of a given arc?

Possible Duplicate: How to calculate the coordinates of the middle point of a given arc? I am trying to calculate the green sides of this triangle: I know/have: the arc length, the arch base, the radius, and the h (distance from the red dot to…
Jonas
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Trigonometric Factorization

How can I factorize this expression: $\sin(x) + \cos(y)$? I've entered this input in Mathemetica: TrigFactor[Sin[x] + Cos[y]] and the output was: $$ 2\sin\left(\frac{\pi}{4} + \frac{x}{2} - \frac{y}{2}\right)\sin\left(\frac{\pi}{4} + \frac{x}{2} +…
kr85
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can't seem to understand $\sin{\theta} = y$ on a unit circle

So I've been working very hard on my trigonometry on khan academy. However I'm constantly getting stumped by one type of question in particular. There is some fundamental flaw in my understanding. I know what the unit circle is completely and why…
gideon
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Solving for an angle

I was never good in trigonometry. I have a rectangle with dimensions $L_1$ and $W_1$. I want to rotate it so that it fits inside another rectangle with dimensions $L_2$ and $W_2$. I need to find the angle. I have worked out the formula that I need…
LeppyR64
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If $\sin( 2 \theta) = \cos( 3)$ and $\theta \leq 90°$, find $\theta$

Find $\theta\leq90°$ if $$\sin( 2 \theta) = \cos( 3)$$ I know that $\sin 2\theta = 2\sin\theta\cos \theta$, or alternatively, $\theta = \dfrac{\sin^{-1}(\cos 3)}{2}$. Can somebody help me?
burm1
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Show that $(7\cos(x)-\sin(x))^2=A\cos(2x)+B\sin(2x)+C$ for some integers $A,B,C$

How do you solve this question?:$$(7\cos(x)-\sin(x))^2=A\cos(2x)+B\sin(2x)+C$$ is for all $x$. Here $A$, $B$ and $C$ is constants. I need to know $A$, $B$ and $C$ to pass this. They are integers. I got this far: (LS = left side) $$LS = …
Olof
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