Question

Solve on the interval [0,2π):
4 csc x+1 = -3

A. 2π/3, 4π/3
B. π/6, 5π/6
C. 3π/2
D. 7π/6, 11π/6

***My Answer: B***
Not too sure though. Please help!

Answer 1

well first subtract the 1 from the first side to get 4 csc x = -4 and then divide each side by 4 to get csc x = -1, then you know that csc x = 1/sin x so (1/sin x)=-1. If you simplify this algebraically it is sin x = -1 which is true only at 3pi/2, therefore you are correct.

Answer 2

Great! Thank you so much!