Question

Find all solutions in the interval 0° ≤ θ < 360° for 2sin θ − √3=0.

a) 30°, 150°
b) 45°, 135°
c) 60°, 120°
d) 90°, 180°

Answer 1

The equation 2sin(θ) - √3 = 0 has solutions where sin(θ) equals √3/2, which occur at 60° and 120° within the range 0° to 360°.

Step-by-step explanation:

The equation to solve is 2sin(θ) - √3 = 0. First, isolate the sine function: sin(θ) = √3/2. The sine of an angle equals √3/2 at 60° (π/3 radians) and 120° (2π/3 radians) in the interval 0° ≤ θ < 360°. Therefore, the solutions in the given interval are 60° and 120°, which corresponds to option c).