# Sine of Angle plus Right Angle

## Theorem

$\sin \paren {x + \dfrac \pi 2} = \cos x$

## Proof

 $\ds \sin \paren {x + \frac \pi 2}$ $=$ $\ds \sin x \cos \frac \pi 2 + \cos x \sin \frac \pi 2$ Sine of Sum $\ds$ $=$ $\ds \sin x \cdot 0 + \cos x \cdot 1$ Cosine of Right Angle and Sine of Right Angle $\ds$ $=$ $\ds \cos x$

$\blacksquare$