Cosine of Complement equals Sine/Proof 4
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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