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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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Exact value of $\tan 50^\circ$

Directly related to: What is $\tan50^\circ$ $50^\circ = \frac{5\pi}{18} $ is a rational multiple of $\pi$. Therefore should be related to the ninth roots of unity $e^{\pi i /18}$, but how does one compute the exact value ? EDIT I will settle for…
cactus314
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find p,q to the expression A does not depend on x?

Find $p,q$ to the expression $A = p (\cos^{8}x-\sin^{8}x) + 4(\cos^{6}x-2\sin^{6}x) + q\sin^{4}x$ does not depend upon $x$
Jung Hyun Ran
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Proof of a trigonometric identity

I need to prove that: $$1+\cos(a+b)-\cos(a-b)=\cos^2(a)+\cos^2(b)$$ I tried to start from both ways but it always took me back to the same one again I tried also to prove that their - equal zero but I didn't work also
user153235
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What's the multiplier value inside a trig function called?

I'm trying to figure out what the b-value is called? y=sin(bx) I've heard some say that it's the frequency or angular frequency, but if my x-values are radian values and not time then what would "b" be called? Angular frequency seems more accurate…
tazboy
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Equations of cosine

where $cos5\theta=16cos^5\theta-20cos^3\theta+5cos\theta$ This is the question I don't understand, and I don't undersatnd the markscheme either. This question is the fifth part of a few, but here are the previous questions. The mark scheme for e…
Jim
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Trigonometry problem cosine identity

Let $\cos^6\theta = a_6\cos6\theta+a_5\cos5\theta+a_4\cos4\theta+a_3\cos3\theta+a_2\cos2\theta+a_1\cos\theta+a_0$. Then $a_0$ is (A) $0$ (B) $\frac{1}{32}$ (C) $\frac{15}{32}$ (D) $\frac{10}{32}$ Any hints on how to approach this?
square_one
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Angle addition formula for cotangent when three angles are being added

$$\cot(x+y+z) = \frac{\cot (x) \cot (y) \cot (z) - (\cot (x)+\cot (y)+\cot (z))}{\cot (x)\cot(y)+\cot(y)\cot(z) + \cot(x)\cot(z) - 1 }$$ I know the addition theorem for two variables, but what to do when you have 3 variables in the argument.
VVV
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How $\tan{\frac{A}{2}}\tan{\frac{B}{2}}=\frac{1}{2}$,then find $\angle C$

In $\Delta ABC$, if $$\tan{\dfrac{A}{2}}\tan{\dfrac{B}{2}}=\dfrac{1}{2}\\\sin{\dfrac{A}{2}}\sin{\dfrac{B}{2}}\sin{\dfrac{C}{2}}=\dfrac{1}{10}$$ Find the $\angle C$ My try:…
math110
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Prove this identity: $ \tan(2x)-\sec(2x) =\tan(x-\pi/4)$

I've been having a time with this problem. I tried to start with the left side but I hit a dead end quick... I then tried the right side and had a little more luck but I've hit a block. I first used the tan difference identity then converted…
user450
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Solving a trigonometric equation

Can someone help me to solve this problem? Find all number pairs $x,y$ that satisfy the equation: $$\tan^4(x) + \tan^4(y) + 2\cot^2(x)\cot^2(y) = 3 + \sin^2(x+y)$$
user34304
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What is $\cos(k \pi)$?

I want to ask question for which I have been finding answer for. Please could anyone explain me why $\cos(k \pi) = (-1)^k$ and also explain me same for $\sin(k \pi)$?
user3215228
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Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?

Why $\cos(-\theta)$ gives positive values while in case of sine it is negative? I mean $\cos(-\theta) = +\cos(\theta)$ $\sin(-\theta) = -\sin(\theta)$ $\tan(-\theta) = -\tan(\theta)$ and please explain General Angles in simple worlds?
Zubair
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What is this trigonometric expression equal to?

If $\frac{cos{x}}{cos{y}}=\frac{a}{b}$, then $(a\times tan{x}+b\times tan{y})$ equals (A)$(a+b)cot{\frac{x+y}{2}}$ (B)$(a+b)tan\frac{x+y}{2}$ (C)$(a+b)(tan\frac{x}{2}+tan\frac{y}{2})$ (D)$(a+b)(cot\frac{x}{2}+cot\frac{y}{2})$ I believe know the…
user140087
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Why is cosine a sine function with offset pi/2?

I was looking at this question and stumbled across this answer stating that the picture proves "Why cosine is simply sine but offset by pi/2 radians" I realized I don't know why this is true. So! Why is cosine sine with an offset pi/2?
Dudemanword
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Is there any other method to solve $\sin x -\sqrt 3 \cos x=1$?

Consider $$ \sin x -\sqrt 3 \cos x=1 $$ for $0\leq x \leq 2\pi$. I solved it by converting $\sin x -\sqrt 3 \cos x$ to $2\sin(x-\pi/3)$ as follows \begin{align*} \sin x -\sqrt 3 \cos x &= r\sin(x-\theta)\\ &= r\sin x\cos\theta -r \cos…
kiss my armpit
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