Sine in terms of Cosine

Theorem
Let $x$ be an real number.

Then:

where $\sin$ denotes the sine function and $\cos$ denotes the cosine function.

Proof
Also, from Sign of Sine:
 * If there exists integer $n$ such that $2 n \pi < x < \left({2 n + 1}\right) \pi$, $\sin x > 0$.
 * If there exists integer $n$ such that $\left({2 n + 1}\right) \pi < x < \left({2 n + 2}\right) \pi$, $\sin x < 0$.

Also see

 * Trigonometric Functions in terms of each other