Question

Find the measure of angle θ in the following when θ is acute.

tan 3θ − 1 = 0

Answer 1

Given:

tan 3θ − 1 = 0

tan 3θ = 1

tan x = 1 → x = 45° + 180°

Since θ is acute, 0° < θ < 90° ⇒ 0° < 3θ < 270°

In this range the allowable values are 

3θ = 45° or 225°

`θ = (45°)/3 = 15° or θ = (225°)/3 = 75°`

θ = 15° or θ = 75°