Solve the equation for 𝜃 if 0° ≤ 𝜃 < 360°. (Enter your answers as a comma-separated list.) 8 sin 𝜃 − 4 csc 𝜃 = 0

Answer 1

cscx = 1/sinx

8sinx - 4cscx = 0

2sinx -cscx= 0

2sinx -1/sinxx = 0 multiply by sinx

2sin^2x - 1 = 0

sin^2x = 1/2

sinx = + or - sqr(1/2) = sqr2/2

x = 45, 135, 225, or 315 degrees

or

x = pi/4, 3pi/4, 5pi/4 or 7pi/4

Answer 2

2sinθ - 1/sinθ = 0; 2sin²θ - 1 = 0; cos2θ = 0; 2θ = 90° + 180°n; θ = 45° + 90°n, n = 0, ± 1, ± 2, ...

θ = 45°, 135°°, 225°, 315°