Cosine of Complement equals Sine/Proof 1

Theorem

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

Proof

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

\(=\)

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

Cosine of Difference

\(\ds \)

\(=\)

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

Cosine of Right Angle and Sine of Right Angle

\(\ds \)

\(=\)

\(\ds \sin \theta\)

$\blacksquare$