Sine and Cosine of Conjugate Angles

Theorem

Sine of Conjugate Angle

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

where $\sin$ denotes sine.

That is, the sine of an angle is the negative of its conjugate.

Cosine of Conjugate Angle

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

where $\cos$ denotes cosine.

That is, the cosine of an angle equals its conjugate.