Can you please help me with this question?

Question

It is given that sin A = k, where A is an angle measured in radians and π < A < 3π/2. If sin B = k, which of the following could be the value of B?

1. (A) A - π
2. (B) π + A
3. (C) 2π - A
4. (D) 3π - A

Answer 1

Here is a picture of the unit circle that might help:

Notice that angle A (in red) must be in quadrant 3 and that the y-value (k) of the point on the unit circle is sin(A). I've drawn the only other point on the unit circle where the y-value (k) is the same in green (in Q4)

A - π would put us in Q1 and that isn't right. π + A would put us at the same place in Q1. 2π - A would put us in Q2 and would also be incorrect. But 3π - A puts us right at the green dot.