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Engineering LibreTexts

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:

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

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