Solve the equation, where 0° ≤ x < 360°. Round approximate solutions to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

Question

3 sin x − 3 cos x = 1

Answer 1

3sinx = 1 + 3cosx
square both sides
9sin^2 x = 1 + 6cosx + 9cos^2 x
9(1 - cos^2 x) = 1 + 6cosx + 9cos^2 x
9 - 9cos^2 x = 1 + 6x + 9cos^2 x
18cos^2 x + 6x - 8 = 0
9cos^2 x + 3x - 4 = 0
cosx = ( -3 ± √153)/18
= -.85385 or .5205

if cosx = -.85385
x = 148.6° or x = 211.4°

if cosx = .5205
x = 58.6° or x = 301.4°

BUT , since we squared our equation, ALL solutions must be verified in the original equation.
Using my calculator, only x = 58.6° and x = 211.4° actually worked in the original equation.