The graph of y = sine (x minus StartFraction 3 pi Over 2 EndFraction) is the graph of the y = sin(x) shifted in which direction? StartFraction 3 pi Over 2 EndFraction units to the left
StartFraction 3 pi Over 2 EndFraction units to the right
StartFraction 3 pi Over 2 EndFraction units up
StartFraction 3 pi Over 2 EndFraction units down

shifted by  3*pi/2 units to the right.

Step-by-step explanation:

Here we have:

y = sin(x - 3*pi/2)

now, you need to remember this:

if we have y = f(x)

then y' = f(x - A) is the graph of y, shifted A units to the right (where A is a positive number).

If A is negative, the shift is to the left.

Then in this case, we have:

sin(x) > sin( x - 3*pi/2)

A = 3*pi/2

Then we have the graph shifted by  3*pi/2 units to the right.