Cosine of Right Angle

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Theorem

$\cos 90^\circ = \cos \dfrac \pi 2 = 0$

where $\cos$ denotes cosine.


Proof

A direct implementation of Cosine of Half-Integer Multiple of Pi:

$\forall n \in \Z: \cos \left({n + \dfrac 1 2}\right) \pi = 0$

In this case, $n = 0$ and so:

$\cos \dfrac 1 2 \pi = 0$

$\blacksquare$


Also see


Sources