How do you graph $y = 2 sin (x + \frac{π}{2}) - 3$ $y=2sin(x+pi/2)-3$ ?

Question

2404 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-06T14:46:32

This is relatively simple. See below.

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

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

How do you graph y=2sin(x+π2)−3 y=2sin(x+pi/2)-3?