Sine of Supplementary Angle

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Theorem

$\sin \paren {\pi - \theta} = \sin \theta$

where $\sin$ denotes sine.


That is, the sine of an angle equals its supplement.


Proof

\(\displaystyle \sin \paren {\pi - \theta}\) \(=\) \(\displaystyle \sin \pi \cos \theta - \cos \pi \sin \theta\) Sine of Difference
\(\displaystyle \) \(=\) \(\displaystyle 0 \times \cos \theta - \paren {-1} \times \sin \theta\) Sine of Straight Angle and Cosine of Straight Angle
\(\displaystyle \) \(=\) \(\displaystyle \sin \theta\)

$\blacksquare$


Also see


Sources