Sine of Complement equals Cosine/Proof 1

Theorem

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

Proof

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

\(=\)

\(\ds \sin \frac \pi 2 \cos \theta - \cos \frac \pi 2 \sin \theta\)

Sine of Difference

\(\ds \)

\(=\)

\(\ds 1 \times \cos \theta - 0 \times \sin \theta\)

Sine of Right Angle and Cosine of Right Angle

\(\ds \)

\(=\)

\(\ds \cos \theta\)

$\blacksquare$