Question

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

Answer 1

Amplitude `= 2`

Period `= pi`

Phase shift `= -(pi/ 4)` `color(white)(aaa)(pi/4)` to the left.

Vertical shift `= 3`

Explanation:

Standard form of equation is `y = a sin(bx + c) + d`

Given = `y = 2 sin (2x + pi/2) + 3`

Amplitude `= a = 2`

Period `= (2pi) / |b| = (2pi) / 2 = pi`

Phase shift `= - c / b = -(pi/2) / 2 = -(pi/ 4)` `color(white)(aaa)(pi/4)` to the left.

Vertical shift `= d = 3`

graph{2sin(2x+(pi/2))+3 [-10, 10, -5, 5]}