Sine of Complement equals Cosine/Proof 1
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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 | |||||||||||
\(\ds \) | \(=\) | \(\ds \cos \theta\) |
$\blacksquare$