Sine of Supplementary Angle

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 $\displaystyle$ $=$ $\displaystyle \sin \theta$

$\blacksquare$