Euler's Formula/Real Domain

Theorem
Let $\theta \in \R$ be a real number.

Then:
 * $e^{i \theta} = \cos \theta + i \sin \theta$

where:
 * $e^{i \theta}$ denotes the complex exponential function
 * $\cos \theta$ denotes the real cosine function
 * $\sin \theta$ denotes the real sine function
 * $i$ denotes the imaginary unit.

Also known as
Euler's Formula in this and its corollary form are also found referred to as Euler's Identities, but this term is also used for the specific example:
 * $e^{i \pi} + 1 = 0$

It is wise when referring to it by name, therefore, to ensure that the equation itself is also specified.