Versed Sine Function is Even

Theorem

The versed sine is an even function:

$\forall \theta \in \R: \map \vers {-\theta} = \vers \theta$

Proof

\(\ds \map \vers {-\theta}\)

\(=\)

\(\ds 1 - \map \cos {-\theta}\)

Definition of Versed Sine

\(\ds \)

\(=\)

\(\ds 1 - \cos \theta\)

Cosine Function is Even

\(\ds \)

\(=\)

\(\ds \vers \theta\)

Definition of Versed Sine

$\blacksquare$