Relationship between e, sin and cos

Converting from e to sin/cos

It is often useful when doing signal processing to understand the relationship between e, sin and cos. Sometimes difficult calculations involving even or odd functions of $e$ can be greatly simplified by using the relationship to simplify things. The relationship is as follows: $e^{j\theta }=cos(\theta )+j*sin(\theta ).$

Converting from sin/cos to e

The reverse conversion is also often helpful:

$cos(\theta )=\frac{e^{j\theta }+e^{-j\theta }}{2}$

$sin(\theta )=\frac{e^{j\theta }-e^{-j\theta }}{2j}$