The function y=sin(x-p)+d has a vertical translation of -3 and passes through the point (pi/6, -2). Determine the values of p and d

My attempt

d= -3

-2= sin (pi/6 - p) -3

1 = 1/2 - sinp

1-1/2= - sinp

1/2= - sinp

-1/2= sinp

The question didn't specify a domain so how would I find the value of p?