In the 2nd Quadrant, SINE is the only Positive.

Where θ is 30 for the first quadrant and

 150 in the 2nd quadrant, which makes COSINE negative 

Sin θ = \(\frac{1}{2}\)

 θ = Sin\(^{-1}(\frac{1}{2}\)) = 30º which is positive in the first quadrant

Sin 30 = Sin 150, i.e, (180 - 30), which is also positive in the second quadrant.

BUT Cos θ = -\(\frac{\sqrt{3}}{2}\)

 θ = Cos\(^{-1}\)(-\(\frac{\sqrt{3}}{2}\)) = 150º which is in the second quadrant but negative

Hence, θ = 150º