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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.

29665 questions
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Solving Trigonometric Equation

I'm trying to solve the following equation for $t$ in the first cycle $0.8=-1.2\sin(2t)+0.8\cos(t)$ I've got it down to $0.8=[\cos(t)](0.8-2.4\sin(t))$ Is there any algebraic way to continue this equation to solve for $t$?
Paul Belardi
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Solve this trigonometric equation. $\frac{1}{\sqrt2}(\sin(\theta)+\cos(\theta))=\frac{1}{\sqrt2}$

I tried solving this equation as follows where $0\leq\theta\leq2\pi$: $$\frac{1}{\sqrt2}(\sin(\theta)+\cos(\theta))=\frac{1}{\sqrt2}$$ Divide both sides by $\frac{1}{\sqrt2}$. $$\sin(\theta)+\cos(\theta)=1$$ Divide both sides by…
lightningC00kie
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Prove $\tan(\frac{x}{2}) = \frac{\sin x}{1 + \cos x} $ using the quadratic formula

I am trying to prove the fact that $\tan \frac{x}{2} = \frac{1-\cos x}{\sin x}$ or alternatively $\tan \frac{x}{2} = \frac{1- \cos x}{\sin x}$. (I understand that it can be proved using the half-angle identities of $\sin$ and $\cos$ but I want to…
Saran Wrap
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Given 2 sides of a triangle find cosine of an angle

I am studying A level maths on my own as an interest. I have the following problem: In $\triangle ABC, AB = 9 cm, AC = 12 cm, \angle B = 2\theta, \angle C = \theta.$ Without using tables or calculators find $\cos\theta$ and the length of BC. Using…
Steblo
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Trigonometric Functions And Identities Question .

If $A$ , $B$ and $C$ are the angles of a triangle , I have to show that : $ \tan^2 \cfrac{A}{2} + \tan^2 \cfrac{B}{2} + \tan^2 \cfrac{C}{2} \ge 1 $ . I had only arrived at $A+B+C = \pi $ , thus $\cfrac{A}{2} + \cfrac{B}{2} + \cfrac{C}{2} =…
Kushashwa Ravi Shrimali
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Confusing question: try and prove that $x -\tan(x) = (2k+1)\frac{\pi}{2}$ has no solution in $[\frac{3\pi}{4},\frac{5\pi}{4}]$

I am trying to show that $x - \tan(x) = (2k+1)\frac{\pi}{2}$ has no solution in $[\frac{3\pi}{4},\frac{5\pi}{4}]$. However, I seem to be stuck as I don't know where to begin. The only sort of idea is that if I were to draw a graph of $\tan x$ and…
user38268
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Solving $\sin[\cot^{-1}(x + 1)]=\cos[\tan^{-1}x]$ in two ways gives contradictory results

I came across this problem to solve for $x$: $$\sin[\cot^{-1}(x + 1)]=\cos[\tan^{-1}x]$$ I tried to do it initially by converting the cosine term on the right to sine by using $\sin(\frac{\pi}{2}-x)=\cos x$, but for some reason this doesn't…
OmG
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Name of functions that are similar to atan2

There was a grouping I saw once of functions that are similar to atan2 where the Y result can only ever be below 1 and over -1 and the closer the value is to the maximum or minimum the longer it takes to reach it on the X axis (until infinity). Does…
dimiguel
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Find all $(x,a,b,c)\in \mathbb{Q}_+\times\mathbb{N}^{*3}$ such that $\cos(\pi x)=\frac{\sqrt {a}+b}{c}$

We will assume that $0<\pi x<\frac{\pi}{2}$ or $0
JPF
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Representation of Tangent function on unit circle

I have found a interesting website in Google. It represents tangent function of a particular angle as the length of a tangent from a point that is subtending the angle.I thought it is really an amazing result. But I can't digest it because I don't…
Mathematical Curiosity
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Solve : $2\sin^3 (x) = \cos (x)$

Solve : $2\sin^3 (x) = \cos (x)$ How to solve the above equation? I tried, but failed to succeed. Graph of the following equation But how to solve the equation without graph?
Kaushik
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Why is $g = \sum_{k=1}^n $ $\sum_{l=1}^n cos(g_k-g_l)$ always non-negative?

Why is $g = \sum_{k=1}^n $ $\sum_{l=1}^n cos(g_k-g_l)$ always non-negative? g is the magnitude square of the complex-valued function, f, defined below, so it is , for sure, non-negative, but I have such a hard time accepting its non-negativity by…
erfaun
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How to solve $\cos(\sin^{-1}(-3/5))$?

I'm stuck with question $$\cos\Bigl(\sin^{-1}\Bigl(-\frac35\Bigr)\Bigr)$$ I looked for the answer in the book and it is $\frac45$ I tried solving it using the formula $\sin^2x+\cos^2x=1$ and I also got $\frac45$ as the answer but I got it by…
Mad Dawg
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A strange trigonometric identity

In this paper, equation (4.5), the authors state the trigonometic identity $$ \sin\left( \frac{n\pi }{1-\theta} \right) = (-1)^{n} \sin\left( \frac{n\pi \theta}{1-\theta}\right) $$ Nothing like it is on Wikipedia's list of trigonometric identities.…
user14717
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Solving $\sin(x)-\cos(x)=1$

Solving $$\sin(x)-\cos(x)=1$$ for $x$. I used Pythagoras' Theoream and $$C\sin(x+\alpha)=A\sin(x)+B\cos(x)$$ where $A=1$ and $B=-1$, and I obtained $$C=\sqrt{2}$$ $$\alpha = \dfrac{\pi}{4}$$ and substituted…
Friedrich
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