Question

Find θ if 0° < θ ≤ 90°.

sin θ = 3 sin 30° − 4 sin³ 30°

Answer 1

Given:

0° < θ ≤ 90°.

sin θ = 3 sin 30° − 4 sin³ 30°

Step 1:

`sin 30° = 1/2`

`sin^2 30° = (1/2)^3 = 1/8`

Step 3:

3 sin 30°

 = `3 ⋅ 1/2 = 3/ 2`

= 4 sin³ 30° 

= `4 ⋅ 1/8 = 4/8`

= `1/2`

Step 4:

`sin θ = 3/2 − 1/2`

= `(3 − 1)/2`

= `2/2 = 1`

sin θ = 1 ⇒ θ = 90°    ... [0° < θ ≤ 90°]

θ = 90°