# How do you graph y=sin(x+pi/2)?

Mar 15, 2017

$y = \cos \left(x\right)$

#### Explanation:

$\sin \left(a + b\right) = \sin \left(a\right) \cos \left(b\right) + \cos \left(a\right) \sin \left(b\right)$

Hence:
$\sin \left(x + \frac{\pi}{2}\right) = \sin \left(x\right) \cos \left(\frac{\pi}{2}\right) + \cos \left(x\right) \sin \left(\frac{\pi}{2}\right)$

$= \sin x \cdot 0 + \cos x \cdot 1 = \cos x$

$\therefore$ the graph of $y$ is the graph of $\cos x$ as below:

graph{cosx [-6.243, 6.24, -3.12, 3.123]}