Radian Trig Equations Help

Question

Solve the trig equation for all values 0 ≤ x ≤ 7

2 sin 2x + √3 = 0

Answer 1

sin(2x) = -√3/2

2x = 4π/3 + 2kπ or 5π/3 + 2kπ, where k = 0, ±1, ±2, ...

x = 2π/3 + kπ, or 5π/6 + kπ

If k = 0, then x = 2π/3 or 5π/6

If k = 1, then x = 5π/3 or 11π/6

Other choices for k give values of x that are either larger than 7 or less than 0.