Sine of Right Angle

From ProofWiki
(Redirected from Sine of 90 Degrees)
Jump to navigation Jump to search

Theorem

$\sin 90 \degrees = \sin \dfrac \pi 2 = 1$

where $\sin$ denotes the sine function.


Proof

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

$\forall n \in \Z: \map \sin {n + \dfrac 1 2} \pi = \paren {-1}^n$

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

$\sin \dfrac 1 2 \pi = \paren {-1}^0 = 1$

$\blacksquare$


Also see


Sources