Characterisation of Sine and Cosine

Theorem
The definitions for sine and cosine are equivalent.

That is:


 * $\displaystyle \sin x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n+1}}{\left({2n+1}\right)!} \iff \sin x = \frac {\text{Opposite}} {\text{Hypotenuse}}$


 * $\displaystyle \cos x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n}}{\left({2n}\right)!} \iff \cos x = \frac {\text{Adjacent}} {\text{Hypotenuse}}$