Dictionary:Euler identity

{{#category_index:E|Euler identity}} The relationships

$e^{i\theta }=cos{\theta }+isin{\theta }={\text{cis}}(\theta )$, $cos\theta ={\frac {e^{i\theta }+e^{-i\theta }}{2}}={\text{cosh}}(i\theta )$ $sin\theta ={\frac {e^{i\theta }-e^{-i\theta }}{2i}}=-i{\text{sinh}}(i\theta )$

where $i={\sqrt {-1}}$.

Named for Leonhard Euler (1707-1783), Swiss mathematician.