If we consider the conventional unit circle, an #angle theta# is measured counter-clockwise from the positive #x-#axis through the four quadrants delimited by #90^@, 180^@,270^@,360^@# respectively. These detemine the #1^(st), 2^(nd), 3^(rd) and 4^(th)# quadrants.
However, we can also measure negative #angle theta# clockwise from the positive #x-#axis where the four quadrants are delimited by #-90^@, -180^@,-270^@,-360^@# as #-theta# passes through the #4^(th), 3^(rd), 2^(nd) and 1^(st)# quadrants around the circle.
Here we are asked in which quadrant #theta = −132^@50'#
#−132^@50'# is between #-90^@ and -180^@# and hence it is in the #3^(rd)# quadrant.
An altenative approach would be to consider:
#−132^@50' = 360^@ −132^@50' =227^@10'#
Since #227^@10'# is betwen #180^@ and 270^@# i.e the #3^(rd)# quadrant
#-> −132^@50'# is in the #3^(rd)# quadrant.
