Which function has a phase shift of π/2 to the right

A.) y = 2sin( 1/2 x + pi )

B.) y = 2sin(2x + pi )

C.) y = 2sin(x + pi/2)

D.) y = 2sin(x - pi )

E.) y = 2sin(2x - pi )

The answer is the option E, which is: E.)[tex] y = 2sin(2x - \pi )
[/tex]

The explanation for this answer is shown below:

1. By definition, you have the phase shift is:

[tex] aSin(bx+c)\\ pshift=-c/b [/tex]

2. When you substitute the values from the function [tex] y = 2sin(2x -\pi ) [/tex], where [tex] c=-\pi [/tex] and [tex] b=2 [/tex], you obtain:

[tex] pshift=-(-\pi )/2=\pi /2 [/tex]