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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Can we solve this equation $\frac{\cos\theta}{\cos{\theta}^2}=k$

I was in doubt that we can solve these type of Equation or not: $\frac{\cos\theta}{\cos{\theta}^2}=k$ where $k$ is a given constant.
Satvik Mashkaria
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Solving $\frac{\sin(\alpha \cdot x)}{\alpha}=\frac{\sin(\beta \cdot x)}{\beta}$

I am looking for a solution for the equation $$\frac{\sin(\alpha \cdot x)}{\alpha}=\frac{\sin(\beta \cdot x)}{\beta}$$ where $\alpha$ and $\beta$ are constants. How do I approach this?
olamundo
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Can three points from a 2-dimensional plane always be transformed to an equilateral triangle in 3-dimensional space?

Given the following three points $$A(x_{1},y_{1})\\ B(x_{2},y_{2})\\ C(x_{3},y_{3})\\$$ and assuming that at least two of these given points are different, how can $z_{1}$, $z_{2}$ and $z_{3}$ be defined so…
Etheryte
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arctan equation question

This question has two parts, I've done the first but I don't understand that second. a. Show that $arctan(\frac{1}{2})+arctan(\frac{1}{3})=\frac{\pi}{4}$ b. Hence, or otherwise, find the value of $arctan(2)+arctan(3)$. The mark scheme has a few…
Jim
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Is there an elegant way to simplify $\frac{\tan(x+20^{\circ })-\sin(x+20^{\circ })}{\tan(x+20^{\circ })+\sin(x+20^{\circ })}$

I wonder how to solve this equation: $$\frac{\tan(x+20^{\circ })-\sin(x+20^{\circ })}{\tan(x+20^{\circ })+\sin(x+20^{\circ })}=4\sin^{2}\left(\frac{x}{2}+10^{\circ }\right)$$ in an elegant/shorter way. My way: $$\frac{\sin(x+20^{\circ…
aric
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How to find out the equation whose roots are trigonometric?

Find out the equation whose roots are $\sin^2 (2\pi/7), \sin^2 (4\pi/7), \sin^2 (8\pi/7)$. I wanted to solve this by firstly finding the equation ,the roots of which are $\sin 2\pi/7,\sin 4\pi/7, \sin 8\pi/7$ .Then i would find the equation wanted…
user142971
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Compute the value of $(\arctan \frac{1}{2}+\arctan \frac{1}{3})/(\operatorname{arccot} \frac{1}{2}+\operatorname{arccot} \frac{1}{3}) $

I'm new to this site I came up with this question in my homeworks: compute : $ \dfrac{\arctan \dfrac{1}{2}+\arctan \dfrac{1}{3}}{\operatorname{arccot} \dfrac{1}{2}+\operatorname{arccot} \dfrac{1}{3}} $ I don't know what idea can help here!What can i…
Master.AKA
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Writing answers to trigonometric equation

I wonder how to write answers to trigonometric equations in more elegant form. For instance if we have $ \displaystyle \sin x = \frac{\sqrt{2}}{2} \vee \sin x=-\frac{\sqrt{2}}{2}$ then I write four cases instead of just one where $\displaystyle…
Gregor
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Fairly simple trig question

Three points at coordinates $(0,c)$, $(p,q)$, $(0,d)$ respectively. The angle at $(p,q)$ between $(0,c)$ and $(0,d)$ is $θ$. Find $d$. P.s. This isn't homework.
Max
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Knowing the hypotenuse and the direction of the adjacent, how would I get the length of the adjacent

I have a good understanding of the basic SohCahToa trig functions, but this kinda stumped me, since I don't have two parts of the information that is needed, here is a example image: https://i.imgur.com/ljztgBm.png I have though of several methods,…
Weeve Ferrelaine
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If $\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$ then $x^2 - 44x - 36 = 0$ holds for $x=\sin 2A$

If $$\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$$ then prove that $$\sin 2A \quad\text{ is a root of }\quad x^2 - 44x - 36 = 0$$ I have no idea how to solve it. Plz help.
user142971
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Triangles having integer sides and integer area.

Find all non-right angled dissimilar triangles having integer sides and integer area simuntaneously. Are there infinitely many such triangle?
Satvik Mashkaria
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What is the value of $\sin 47^{\circ}+\sin 61^{\circ}- \sin25^{\circ} -\sin11^{\circ}$?

After simplification using sum to product transformation equations I keep ending up with $$4\cos36^\circ\cdot\cos7^\circ\cdot\cos18^\circ$$ How do I simplify this to a single term?
Niharika
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Find the value of $(a+b+c)$ when $\cos\theta+\cos^2\theta+\cos^3\theta=1$ and $\sin^6\theta=a+b\sin^2\theta+c\sin^4\theta$

Given: $\cos\theta+\cos^2\theta+\cos^3\theta=1$ and $\sin^6\theta=a+b\sin^2\theta+c\sin^4\theta$ Then find the value of $(a+b+c)$
Rudstar
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Is $\sqrt{1-\sin ^2 100^\circ}\cdot \sec 100^\circ = 1$ or $-1$?

The equation will simplify to \begin{align} & = \sqrt{\cos^2 100^\circ}\cdot \sec100^\circ \\[8pt] & = \cos100^\circ\cdot\sec100^\circ \\[8pt] & = 1 \end{align} But the answer key says that the correct answer is $-1$?
Niharika
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