Sine of Complement equals Cosine

Theorem
$$\cos \theta = \sin \left({\frac \pi 2 - \theta}\right)$$

where $$\frac \pi 2 - \theta$$ is the complement of $$\theta$$.

Proof

 * From Sine and Cosine are Periodic on Reals, we have $$\sin \left({x + \frac \pi 2}\right) = \cos x$$;
 * Also from Sine and Cosine are Periodic on Reals, we have $$\sin \left({x + \pi}\right) = \cos \left({x + \frac \pi 2}\right) = -\sin x$$;
 * From Basic Properties of Sine Function, we have $$\sin \left({x + \frac \pi 2}\right) = - \sin \left({- x - \frac \pi 2}\right)$$.

So:

$$ $$ $$ $$

Note
Compare Sine equals Cosine of Complement.