Sine of Complement equals Cosine/Proof 2

Theorem

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

Proof

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

\(=\)

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

Sine Function is Odd

\(\ds \)

\(=\)

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

Cosine of Angle plus Right Angle

\(\ds \)

\(=\)

\(\ds \cos \theta\)

$\blacksquare$