What is the period of...?

Question

The equation y=2-3sin(pi/4)(x-1) has a fundamental period of....?

Answer 1

Did you mean:
y=2-3sin((pi/4)(x-1)) ?

Recall that the period of sin(x) is 2*pi

Since we are making x smaller by a factor of pi/4, the period therefore must get bigger by a factor of 1/(pi/4) = 4/pi

So our new period is 2*pi*(4/pi) = 8

Answer 2

This isn't periodic! At least not the way you wrote it.
Note that sin(pi/4) = sqrt(2)/2
So your equation is
y = -3sqrt(2)/2(x-1) + 2,
which is the equation of a line, not a sinusoid.