Solve the following trigonometric equation assuming that 0 ≤ 𝜃 < 2𝜋. (Enter your answers as a comma-separated list.) 2 − 4 sin(𝜃) = 1 − 6 sin(𝜃)

Answer 1

2-4sinT = 1-6sinT

let x = sinT

2-4x = 1-6x

2x =-1

x =-1/2

sinT =-1/2

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

theta = the angle whose sine = -1/2

theta is in quadrant III or IV where all sines are negative

theta = 330 or 210 degrees

theta = 210,330 or 7pi/6, 11pi/6

check the answers

2-4sin210=1 -6sin210

2-4(-1/2) = 1- 6(-1/2)

2+2 = 1+3

4 =4