12.1: Trigonometry
- Page ID
- 24860
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\[e ^ { j \theta } = \cos \theta + j \sin \theta \nonumber \]
\[\cos \theta = \frac { 1 } { 2 } \left( e ^ { j \theta } + e ^ { - j \theta } \right) \nonumber \]
\[\sin \theta = \frac { 1 } { j 2 } \left( e ^ { j \theta } - e ^ { - j \theta } \right) \nonumber \]
\[\cos ^ { 2 } \theta = \frac { 1 } { 2 } + \frac { 1 } { 2 } \cos 2 \theta \nonumber \]
\[\sin ^ { 2 } \theta = \frac { 1 } { 2 } - \frac { 1 } { 2 } \cos 2 \theta \nonumber \]
\[\sin (a \pm b)=\sin a \cos b \pm \cos a \sin b \nonumber \]
\[\cos (a \pm b)=\cos a \cos b \mp \sin a \sin b \nonumber \]
Hyperbolic trigonometric functions:
\[\sinh \theta=\frac{1}{2}\left(e^{+\theta}-e^{-\theta}\right) \nonumber \]
\[\cosh \theta=\frac{1}{2}\left(e^{+\theta}+e^{-\theta}\right) \nonumber \]