# How do you graph  y=2sin(x+pi/2)-3?

May 6, 2017

This is relatively simple. See below.

#### Explanation:

1. Find the parent function of the graph. This should be: $y = \sin x$.
2. Now, identify all the transformations applied to the graph:
(a) Vertical stretch by a factor of 2
(b) Horizontal shift to the left by $\frac{\pi}{2}$
(c) Vertical shift down by 3
3. You can now graph, either by individually applying each transformation above or using a mapping formula. For instance,
$\left(x , y\right) \to \left(x - \frac{\pi}{2} , 2 y - 3\right)$
$\left(0 , 0\right) \to \left(- \frac{\pi}{2} , - 3\right)$
$\left(1 , \frac{\pi}{2}\right) \to \left(0 , \pi - 3\right)$
etc.

After you've obtained all the points, you can graph.