Find all exact solutions on the interval 0 ≤ x < 2π. (Enter your answers as a comma-separated list.) csc2(x) − 5 = −1

Answer 1

csc^2(x) = 4

1 = 4*sin^2(x)

1/4 = sin^2(x)

+or- 1/2 = sin(x)

sine is 1/2 at flavors of 30 degrees

30, 150, 210, 330

Answer 2

csc2(x)-5--1

csc2(x)=4

1/sin2(x)=4

sin2(x)=1/4

sin(x)=+/- 1/2

in the domain 0<=x,<2pi:

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