Đẳng thức lũy thừa số phức

$\sin \theta =\mathrm{R}\mathrm{e}(e^{i\theta })=\frac{e^{i\theta }-e^{-i\theta }}{2i}$

$\cos \theta =\mathrm{I}\mathrm{m}(e^{i\theta })=\frac{e^{i\theta }+e^{-i\theta }}{2}$

$\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{e^{2i\theta }-1}{i(e^{2i\theta }+1)}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{2i}{e^{i\theta }-e^{-i\theta }}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{2}{e^{i\theta }+e^{-i\theta }}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{i(e^{2i\theta }+1)}{e^{2i\theta }-1}$