#1**+3 **

We will have the following form

y = Asin (Bx + C ) + D

A = the amplitude = 2

The period = 1 / frequency = 1 / (1/ [4pi] ) = = 4pi

B = [ 2pi] / period = [ 2pi ] / [ 4pi] = 1/2

C = phase shift = there is none....so.....C = 0

D = the shift up/down

Because the midline of the normal sine function is y = 0.....then the midline y = 2 shifts this up 2 units....so...D = 2

So.....the function is

y = 2sin [ (1/2)x ] + 2

Here is the graph :

https://www.desmos.com/calculator/bmcanvqjfx

CPhill Feb 14, 2019