6.6b Solving Trigonometric Equation (Factorization) January 21, 2022August 22, 2021 by 6.6b Solving Trigonometric Equation (Factorization) Example: Find all the angles that satisfy each of the following equations for 0° £ x £ 360°. (a) cot x = − 2 cos x (b) 3 sec x = 4 cos x (c) 16 tan x = cot x Solution: (a) cot x = − 2 cos x cos x sin x = − 2 cos x cos x = − 2 cos x sin x cos x + 2 sin x cos x = 0 cos x ( 1 + 2 sin x ) = 0 cos x = 0 x = 90 ∘ , 270 ∘ 1 + 2 sin x = 0 sin x = − 1 2 Basic ∠ = 3 0 ∘ x = ( 180 ∘ + 30 ∘ ) , ( 360 ∘ − 30 ∘ ) x = 210 ∘ , 330 ∘ ∴ x = 90 ∘ , 210 ∘ , 270 ∘ , 330 ∘ (b) 3 sec x = 4 cos x 3 cos x = 4 cos x 3 = 4 cos 2 x cos 2 x = 3 4 cos x = ± 3 2 Basic ∠ = 30 ∘ x = 30 ∘ , ( 180 ∘ − 30 ∘ ) , ( 180 ∘ + 30 ∘ ) , ( 360 ∘ − 30 ∘ ) x = 30 ∘ , 150 ∘ , 210 ∘ , 330 ∘ (c) 16 tan x = cot x 16 tan x = 1 tan x tan 2 x = 1 16 tan x = ± 1 4 Basic ∠ = 14.04 ∘ x = 14.04 ∘ , ( 180 ∘ − 14.04 ∘ ) , ( 180 ∘ + 14.04 ∘ ) , ( 360 ∘ − 14.04 ∘ ) x = 14.04 ∘ , 165.96 ∘ , 194.04 ∘ , 345.96 ∘