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.

29665 questions
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Finding $\tan B$ and $\tan(A+B)$

So I know that $$ \tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \tan(B)}, $$ but I don't know how to find $\tan(B)$ for the following problem: If $\tan A = 2/3$ and $\sin B = 5/\sqrt{41}$ and angles $A$ and $B$ are in Quadrant I, find the value…
ToxicTechnetium
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($\cos^4x$)($\sin^2x$) in terms of first power of cosine

I believe that I have his correct but if someone could check it and see that'd be great. Here's a pic!
King Squirrel
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Why do you have to begin with the largest angle or side when using law of cosines

Explain why you should always start with the largest angle or the largest side when using law of cosines. I don't understand why but my professor says so.
King Squirrel
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Computing Points in 3D Space

I am working on a project for my 3D Graphics class. The project is built with C++ and OpenGL / Glut. Basically, I create a horizontal rectangle window, subdivided into two squares. On the left, I have a two dimensional coordinate plane, which allows…
Josh
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Trigonometric substitution

Been out of touch with trigonometry for some time now. Need help proving this expression. $$\sin^{2}\left(\frac{x}{2}\right) = \frac{1}{2}(1-\cos\left(x\right))$$ Any help will be appreciated. Thanks.
Clockwork
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Can I find this trigonometric expression without a calculator?

I know that $\sin A= 0.75$ will give me the answer of $A= 48.6^\circ$ or $\ 131^\circ$. Is there a way to find what $A$ equals manually. Thank you.
user134345
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How to simplify this trignometric expression: $4( 3 \sin \theta)( 3 \cos \theta)$?

I was given a circle with a radius of $3$ and in it was a rectangle and an angle $\theta$ extending from the $x$ axis to up with coordinates of $(3 \cos \theta, 3 \sin \theta)$ and the question asks me to show that the area of the triangle…
user134345
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The Distance Conundrum

I have sometimes wondered about a distance problem that involves travelling along the two triangular sides of distance between two points, then gradually shortcutting the distances into smaller and smaller chunks. I can't quite understand why, when…
betchaboy
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Can someone explain this?

$\sec(x/2) = \cos(x/2)$ I worked on this and got here... (Let (x/2) = u) $\cos u - \sec u = 0$ $\cos u(1 - \sec^2u) = 0$ $\cos u[ -1(-1 + \sec^2u)] = 0$ $\cos u(-\tan^2u) = 0$ So, the solutions would be: $x = pi + 4\pi k, 3\pi + 4\pi k, 0 + 2\pi k$…
King Squirrel
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What is the minimum value of $(\sin x + \cos x + \csc (2x))^3$

What is the minimum value of: $$(\sin x + \cos x + \csc 2x )^3$$ let us consider that $0
maths lover
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How to prove this trig identity?

If $A+B+C=\pi$ then prove:$$\sin^2A+\sin^2B+\sin^2C=2-2\cos A\cos B\cos C$$ I am completely lost on this, please help.
Sawarnik
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Solve $5\sin^2(x) + \sin(2x) - \cos^2(x) = 1$

I tried $$5\sin^2(x) + 2\sin(x)\cos(x)- (1-\sin^2(x)) = 1.$$ Simplifying, $$6\sin^2(x) + 2\sin(x)\cos(x) -2 = 0$$ Then I'm stuck!
timaru
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How to get apparent linear diameter from angular diameter

Say I have an object, whose actual size is 10 units in diameter, and it is 100 units away. I can find the angular diameter as such: $2\arctan(5/100) = 5.725\ $ radians. Can I use this angular diameter to find the apparent linear size (that is, the…
cmal
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How to solve a quadratic in $\sin(t)$ and $\cos(t)$

How can I solve this form of quadratic? It has no $\sin(t)\cos(t)$ term. $$(\cos(t) + p + a)^2 - a^2 + b (\sin(t) + q)^2 = 0$$ Multiplied out: $$\cos^2(t) + 2(a+p)\cos(t) + b\sin^2(t) + 2bq\sin(t) + (p^2 + 2ap + bq^2) = 0$$ I'm at a loss for…
jnm2
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Prove that $\sqrt[3]{\sec\frac{2\pi }{7}} + \sqrt[3]{\sec\frac{4\pi }{7}} + \sqrt[3]{\sec\frac{8\pi }{7}} = \sqrt[3]{8-6\sqrt[3]{7}}$

Prove that: $$\sqrt[3]{\sec\frac{2\pi }{7}} + \sqrt[3]{\sec\frac{4\pi }{7}} + \sqrt[3]{\sec\frac{8\pi }{7}} = \sqrt[3]{8-6\sqrt[3]{7}}$$ Thank you! Avdiu...
user136109
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