Euler’s formula
$$ 1. \ \sin \theta = \frac {1}{2i} \left( e^{i \theta } – e^{-i \theta } \right) $$
$$ 2. \ \cos \theta = \frac {1}{2} \left( e^{i \theta } + e^{-i \theta } \right) $$
$$ 3. \ \tan \theta = i \frac {\left( e^{-i \theta} – e^{i\theta} \right)}{\left( e^{i\theta} + e^{-i\theta} \right)} $$