Question

find all the angles between 0° and 360° which satisfy the equation sin y = 3 cos (y - 30

Answer 1

sin y = 3 cos (y - 30)
siny = 3(cosy cos30 + siny sin30)
siny = 3(√3/2 cosy + 1/2 siny)
-1/2 siny = 3√3/2 cosy
tany = -3√3
tany < 0 in QII and QIV.

Answer 2

Assuming you are working in degrees ...
cos(y-30) = cosycos30 + sinysin30 = (√3/2)cosy + (1/2)siny
= (1/2)(√3cosy + siny)

sin y = 3 cos (y - 30)
siny = (3/2)(√3cosy + siny)
2siny = 3√3cosy + 3siny
siny = -3√3cosy
siny/cosy = -3√3
tany = -3√3
for your 0 ≤ y ≤ 360°
y = 100.9° or y = 280.9°

Answer 3

didn't realize oobleck already posted it,
must have happened while I was working it,
glad we have the same answer

Answer 4

Happens all the time mathhelper :)