Cosine of Complement equals Sine/Proof 2

Theorem

$\map \cos {\dfrac \pi 2 - \theta} = \sin \theta$

Proof

\(\ds \map \cos {\frac \pi 2 - \theta}\)

\(=\)

\(\ds \map \cos {\theta - \frac \pi 2}\)

Cosine Function is Even

\(\ds \)

\(=\)

\(\ds \map \sin {\theta - \frac \pi 2 + \frac \pi 2}\)

Sine of Angle plus Right Angle

\(\ds \)

\(=\)

\(\ds \sin \theta\)

$\blacksquare$