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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How to derive cosine difference formula?

I was asked on a take home quiz to "Derive the Cosine Difference Formula". I've looked for an hour but I've gotten different results this is kind of my last chance.
Michael Antoci
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Finding the height given the angle of elevation and depression.

Please, I need help for this problem. I'm a little confused about it :( From a point A 10ft. above the water the angle of elevation of the top of a lighthouse is 46 degrees and the angle of depression of its image is 50 degrees. Find the height of…
jhong
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How to find $\angle$ b?

How to find $\angle$ b ? The vertices of the triangle are on the foci of the ellipse and on the ellipse. $\angle$ a, the major axis and eccentricity are known.
Andreas
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How to proceed from $\cot(x)\cot(2x)-\cot(2x)\cot(3x)-\cot(3x)\cot(x) = 1$

To prove: $\cot(x)\cot(2x)-\cot(2x)\cot(3x)-\cot(3x)\cot(x) = 1$ My attempt at the…
Aayush Agrawal
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If $A=\sin^{20}\theta +\cos^{48}\theta $ then identify the correct option.

If $A=\sin^{20}\theta +\cos^{48}\theta $, then for all values $\theta$ a) $A\geq 1$ b) $ 0< A\leq 1$ c) $1
R K
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Verify the following identities

I want to verify the following identities: $${\sin^3\alpha-\cos^3\alpha\over \sin\alpha -\cos\alpha} = 1 + \sin\alpha \cos\alpha$$ I feel like I need to work on the first member – the second one looks fine. I can't really figure out how to transform…
Cesare
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If $\alpha= \frac{\pi}{7}$ and also if $\frac{3- \tan^2 (\alpha)}{1 - \tan^2 (\alpha)} = \lambda \cos(\alpha)$. Then find $\lambda$.

Given that $$\frac{3- \tan^2 \left(\dfrac{\pi}{7}\right)}{1 - \tan^2 \left(\dfrac{\pi}{7}\right)} = \lambda \cos\left(\dfrac{\pi}{7}\right)$$ Then find the value of $\lambda$.
Surya Prakash
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In the trigonometric identity $\cos(\frac{\pi}{2} -\theta)$, why are we reflecting the graph in vertical axis.

I was wondering why do we need to reflect the graph in vertical axis in the trigonometric identity: $\cos(\frac{\pi}{2} -\theta) = \sin(\theta)$. It seems that if we only translate the graph of $\cos(\theta)$ by $\frac{\pi}{2}$ it would take the…
Pawel
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If $\arcsin x+\arcsin y+\arcsin z=\pi$,then prove that $(x,y,z>0)x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$

If $\arcsin x+\arcsin y+\arcsin z=\pi$,then prove that $(x,y,z>0)$ $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$ $\arcsin x+\arcsin y+\arcsin z=\pi$, $\arcsin x+\arcsin y=\pi-\arcsin z$ $\arcsin(x\sqrt{1-y^2}+y\sqrt{1-x^2})=\pi-\arcsin…
diya
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Calculate alpha from $\alpha + \sin(\alpha)$ = K

Sorry for the dumb question, but I'm not involved in math. I need to reverse the following formula, to calculate $\alpha$: $$a = b(\alpha + \sin \alpha)/c$$ So I have: $$(\alpha + \sin \alpha)=ac/b = K$$ Since $a$, $b$, $c$ are constant, I put equal…
Tommaso
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$\tan\frac{\pi}{16}+\tan\frac{5\pi}{16}+\tan\frac{9\pi}{16}+\tan\frac{13\pi}{16}$

Find the value of the expression $\tan\frac{\pi}{16}+\tan\frac{5\pi}{16}+\tan\frac{9\pi}{16}+\tan\frac{13\pi}{16}$ I identified that…
Vinod Kumar Punia
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How does $\cos\frac\theta2 = \pm\sqrt{\frac{(1 + \cos \theta)}{2}}$?

Background: I'm studying roots of complex variables (i.e. not homework!), and going through a worked problem from Schaum's Outlines on Complex Variables. In a worked problem, the following equation is presented and assumed the reader knows trig well…
PeteUK
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Use Trigonometry to make a Marksman's Sight

In the Civil War, marksmen used something called a "stadia" which is nothing more than a piece of brass with a triangular hole cut out and a slide with marks of varying distances. Line your target up within the hole, center the slide over it, and…
Ivan Dreka
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if $\sin{(aw)}+\sin{(bw)}+\sin{(cw)}=3$ find $w$ range

let $w$ is postive integer,if there exist $a,b,c(\pi\le a
user223800
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