Please please please answer all Solve on 0 2 pi a sinx 12 c

Please please please answer all!

Solve on [0, 2 pi). (a) sin(x) = -1/2 cos (2x) = Squareroot 2/2 csc^2 (x) = 4

a) sin x = -1/2

x = sin^-1 ( -1/2)

x = 7pi/6 + 2pi*n , 11pi/6 + 2pi*n

x = 7 pi/6 , 11pi/6

b) cos (2x) = sqrt 2/ 2

2x = pi/4 + 2pi*n , 7pi/4 + 2pi*n

x = (pi + 8pi*n )/ 8 , ( 7pi + 8pi*n ) / 8

x = pi/8 , 7pi/8 , 15pi/8 , 9pi/8

c) csc^2(x) = 4

taking square root on both sides

csc x = + - 2

csc x = + 2 , x = pi/6 , 5pi/6

csc x = -2 , x = 7pi/6 , 11pi/6

solutions are

x = pi/6 , 5pi/6 , 7pi/6 , 11pi/6