# 12.1: Trigonometry

- Page ID
- 19622

\[e ^ { j \theta } = \cos \theta + j \sin \theta\]

\[\cos \theta = \frac { 1 } { 2 } \left( e ^ { j \theta } + e ^ { - j \theta } \right)\]

\[\sin \theta = \frac { 1 } { j 2 } \left( e ^ { j \theta } - e ^ { - j \theta } \right)\]

\[\cos ^ { 2 } \theta = \frac { 1 } { 2 } + \frac { 1 } { 2 } \cos 2 \theta\]

\[\sin ^ { 2 } \theta = \frac { 1 } { 2 } - \frac { 1 } { 2 } \cos 2 \theta\]

\[\sin (a \pm b)=\sin a \cos b \pm \cos a \sin b\]

\[\cos (a \pm b)=\cos a \cos b \mp \sin a \sin b\]

**Hyperbolic trigonometric functions:**

\[\sinh \theta=\frac{1}{2}\left(e^{+\theta}-e^{-\theta}\right)\]

\[\cosh \theta=\frac{1}{2}\left(e^{+\theta}+e^{-\theta}\right)\]