
1.12: Inverse Euler formula


Euler's formula gives a complex exponential in terms of sines and cosines. We can turn this around to get the inverse Euler formulas.

Euler’s formula says:

$e^{it} = \cos (t) + i \sin (t)$

and

$e^{-it} = \cos (t) - i \sin (t).$

By adding and subtracting we get:

$\cos (t) = \dfrac{e^{it} + e^{-it}}{2}$

and

$\sin (t) = \dfrac{e^{it} - e^{-it}}{2i}.$

Please take note of these formulas we will use them frequently!