Find the exact value of function csc(150°)

Question

answer choices:

A (√3) / 3

B -√3
C -1

D -2

Answer 1

cosecant is the reciprocal of sine (csc x = 1/sin x), so we need to know the sin, and then we can find the csc. The reference angle for a 150 degree angle is 30 degrees. (Let me know if you need an explanation on reference angles) 150 degrees is in the second quadrant (again, let me know if this needs explanation), where sin (and csc) are both positive.  Since sin 30 is 1/2, then sin 150 is also 1/2.  That means that csc 150 is the reciprocal, which is 2.  I'm pretty sure that either D should be positive 2, or there's a mistake in the answer choices.