Cosine of Zero is One

Theorem

 * $\cos 0 = 1$

where $\cos$ denotes the cosine.

Proof
Recall the definition of the cosine function:


 * $\displaystyle \cos x = \sum_{n \mathop = 0}^\infty \left({-1}\right)^n \frac {x^{2n}}{\left({2n}\right)!} = 1 - \frac {x^2} {2!} + \frac {x^4} {4!} - \cdots$

Thus:


 * $\displaystyle \cos 0 = 1 - \frac {0^2} {2!} + \frac {0^4} {4!} - \cdots = 1$

Also see

 * Sine of Zero is Zero