Cosine of Complement equals Sine/Proof 4

Theorem

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

Proof

Let $\angle xOP$ and $\angle QOy$ be complementary.

Then:

$\angle xOP = \angle QOy$

Hence:

the projection of $OP$ on the $x$-axis

equals:

the projection of $OQ$ on the $y$-axis.

Hence the result.

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Complementary angles