Sine of Complement equals Cosine/Proof 2

Theorem

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


Proof

\(\ds \map \sin {\frac \pi 2 - \theta}\) \(=\) \(\ds -\map \sin {\theta - \frac \pi 2}\) Sine Function is Odd
\(\ds \) \(=\) \(\ds \map \cos {\theta - \frac \pi 2 + \frac \pi 2}\) Cosine of Angle plus Right Angle
\(\ds \) \(=\) \(\ds \cos \theta\)

$\blacksquare$

This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.