Question

Find the angle θ when 0° < θ < 90°.

(tan² θ − 3)(2 sin 3θ − 1) = 0

Answer 1

Step 1:

tan² θ − 3 = 0 or 2 sin 3θ − 1 = 0

tan² θ = 3

tan θ = ± sqrt3

0° < θ < 90°, tangent is positive

tan θ = `sqrt3`

θ = 60°

Step 2:

2 sin 3θ − 1 = 0 ⇒ sin 3θ =

sin x = `1/2` when x = 30°, 150°,...

3θ = 30° → θ = 10°

3θ = 150° ⇒ θ = 50°

θ = 60° & θ = 50°