Trigonometric Functions

Trigonometric Angle Addition Formulas

For any

α, β \in ℝ

:

\begin{matrix} \cos (α + β) & = \cos (α) \cos (β) - \sin (α) \sin (β) \\ \sin (α + β) & = \sin (α) \cos (β) + \cos (α) \sin (β) \end{matrix}

Sine is Odd and Cosine is Even

For any

α \in ℝ

:

\sin (- α) = - \sin (α) and \cos (- α) = \cos (α) .

Sine is Zero on Zero to Pi Only at the Endpoints

If

θ \in [0, π]

, then

\sin (θ) = 0 ⟺ θ = 0 or θ = π

TODO: Add a proof from the unit circle definition of sine.