Power and n-th arguments of trigonometric functions

Calculator for powers and n-fold arguments of sine and cosine

Calculator for calculating powers and n-fold arguments of the trigonometric functions sine and cosine.

n =

Addition theorem for multiples of the argument of sine and cosine

$\sin \left(2x\right)$$=2\sin \left(x\right)\cos \left(x\right)$

$\sin \left(3x\right)$$=3\sin \left(x\right)-4{\sin }^3\left(x\right)$

$\cos \left(2x\right)$$={\cos }^2\left(x\right)-{\sin }^2\left(x\right)$

$\cos \left(3x\right)$$=4{\cos }^3\left(x\right)-3\cos \left(x\right)$

Powers of sine and cosine

${\sin }^2\left(x\right)$$=\frac{1}{2}\left(1-\cos \left(2x\right)\right)$

${\sin }^3\left(x\right)$$=\frac{1}{4}\left(3\sin \left(x\right)-\sin \left(3x\right)\right)$

${\sin }^n\left(x\right)$$=\frac{1}{2^n}\sum _{k=0}^n\left(\begin{array}{c}n\\ k\end{array}\right)\cos \left(\left(n-2k\right)\left(x-\frac{\pi }{2}\right)\right)$

${\cos }^2\left(x\right)$$=\frac{1}{2}\left(1+\cos \left(2x\right)\right)$

${\cos }^3\left(x\right)$$=\frac{1}{4}\left(3\cos \left(x\right)+\cos \left(3x\right)\right)$

${\cos }^n\left(x\right)$$=\frac{1}{2^n}\sum _{k=0}^n\left(\begin{array}{c}n\\ k\end{array}\right)\cos \left(\left(n-2k\right)x\right)$

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