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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$\theta_1 + \theta_2 = -35.5$ how to find the values of those $\theta$s?

I have a problem, I'm trying to solve inverse kinematics problem, but I have hit the wall. I have 2 equation for $$\cos(\theta_2) \cos(\theta_3) - \sin(\theta_2) \sin(\theta_3) = 45.7518$$ and for $$\sin(\theta_3) \cos(\theta_2) + \sin (\theta_2)…
user126448
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Proving double-angle trig identities

I'm having some trouble proving trig identities, this time with the double-angle formula. I want to prove that: $$ \frac{1 + \tan^2 A}{1 - \tan^2 A}=\sec 2A $$ I know that: $$ 1 - \tan^2 A = \frac{2 \tan A}{\tan 2A} $$ But I don't know how to get…
hohner
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Equation $2\cos(x)-3\tan(x)=0$

I solved this equation $2\cos(x)-3\tan(x)=0$ and I got, $\frac{1}{2}=\sin(x)$ and $-2=\sin(x)$. For the first solution I got $\arcsin(1/2)=x, 30°=x$, but second is invalid because the domain of arcsin can be only between $-1$ and…
depecheSoul
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Any reason beyond academics to represent a known constant as variable?

In biomechanics, for calculating joint angles there is a research paper most often referenced and which most of the algorithms are based on http://www.sciencedirect.com/science/article/pii/016794579190046Z#. In the paper, they use sin(beta) and…
user-2147482637
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Solving a particular trigonometric equation

I am wondering if it is possible to solve the equation \begin{equation} \sin(x) = 0.4. \end{equation} If it is possible to solve this, how does one do so?
Ryuzaki
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How to prove this arcsine identity?

In the top of this Wikipedia article for the arcsine distribution it states that $$\frac{2}{\pi} \arcsin(\sqrt{x}) = \frac{\arcsin(2x-1)}{\pi} + \frac{1}{2}$$ Why is this true? I haven't been able to derive this.
user901823
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Equivalent form of sinc function?

My trig is a bit rusty, so here goes: I believe that the sinc function, i.e. $\frac{\sin(\theta)}{\theta}$, where $\theta = \pi x = \frac{\sin(\theta)}{N\tan(\frac{\theta}{N})}$ for sufficiently large values of $N$. I've tested this for values of…
Karl Brotts
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Solving $\sqrt{3\cos^2 x - \sin 2x} = - \sin x$

Please, can you suggest something for solving this equation: I have to find the solutions included in interval $\left[3\pi/2, 2\pi\right]$: $$\sqrt{3\cos^2 x - \sin 2x} = - \sin x$$ This is what I did: $$\begin{array}{crcl} \Longrightarrow &…
wonderingdev
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Trigonometry question (acute angle triangle)

Let $ABC$ be an acute angle triangle. Show that : \begin{equation} \sum _{cyc}(\sin2B+\sin2C)^{2} \sin A \leq 12 \sin A \sin B \sin C \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(*)\end{equation} My try: I think one can start with applying the…
Zia
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Formula for sine-wave that lines up with calendar seasons

I'm using Google Correlate tool to do some research and they have an example graph that is a sine wave that represents winter, the line was called "winter wave". http://www.google.com/trends/correlate/search?e=id:PaHT-seSlg9&t=weekly I was curious…
Pat Grady
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Simplify the expression : $\tan(\theta) +2\tan(2\theta) +2^2\tan(2^2 \theta) +\cdots +2^{14} \tan(2^{14}\theta) +2^{15} \cot(2^{15} \theta)$

How to simplify the expression: $\tan(\theta) +2\tan(2\theta) +2^2\tan(2^2 \theta) +\ldots +2^{14} \tan(2^{14}\theta) +2^{15} \cot(2^{15} \theta)$ I am not getting any clue how to proceed in such problem please suggest it will be of great help ..…
Sachin
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Finding a side given 2 angles and a side (and rationalizing a denominator afterwards)

(In advanced, I apologize for not knowing how to make fractions) Here's the problem: A triangle has side $c = 8$ and angles $A = \pi/4$ and $B = \pi/6$. Find the length of the side opposite $A$. Here's where I'm at so far: Since $A$ is 45 degrees…
Mxyk
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trigonometry identity

I have some problem with proving this identity: $$2\left(1+\cos\alpha \right)-\sin^2\alpha=4\cos^4\frac{\alpha}{2}$$ I tried to start from the right side rewritting it to $(2\cos^2(2\frac{\alpha}{4}))^2$ but it's not working.
Mark
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how to prove $\tan A+\sec A=\frac{1}{(\sec A-\tan A)}$?

how to prove $\tan A+\sec A=\frac{1}{(\sec A-\tan A)}$ ? I already tried: $$\begin{align} \sin A/\cos A+1/\cos A&=1/(\sec A-\tan A)\\ \sin A+1/\cos A&=1/(\sec A-\tan A)\\ \end{align}$$
Jorge Steven
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$\tan2x$ in terms of $\cos x$ alone

This is not exactly a homework question but something I was trying to do to get my basics back on track. I wanted to find $\tan2x$ in terms of $\cos x$ alone. I was able to do it in terms of $\sin x$ alone. $\tan2x = \sin2x/\cos2x$ Since, $\cos2x =…
Kartik Anand
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