Euler's theorem

Euler's theorem is this fun little theorem that appears simple but it is complex. It has a lot to do with complex numbers.

Solving for cos&theta;
Add the two equations together:

$$ e^{jx} + e^{-jx} = 2 \cos \theta \rightarrow \cos \theta = \frac{e^{j\theta}+e^{-j\theta}}{2}$$

Solving for sin&theta;
Subtract the negative equation from the positive equation:

$$ e^{jx} - e^{-jx} = 2j \sin \theta \rightarrow \sin \theta = \frac{e^{j\theta}-e^{-j\theta}}{2j}$$