find all solutions in the interval [0, 2pi) : sin x = ((1/(4 sin x))?

Question

a. (pi/6) , (5pi/6)
b. (7pi/6) , (11pi/6)
c. (pi/3) , (2pi/3) , (4pi/3) , (5pi/3)
d. (pi/6) , (5pi/6) , (7pi/6) , (11pi/6)
e. none of these

Answer 1

correct answer d

this equation is the same as

4 (sin x) ^2 = 1

(sinx)^2 =1/4

sin x = +1/2 or -1/2

this is for d

Answer 2

4 sin^2 x = 1
sin^2 x = 1/4
sin x = 1/2
then include the interval to find the answers.