5.6b Solving Trigonometric Equation (Factorization)

5.6b Solving Trigonometric Equation (Factorization)
 
Example:
Find all the angles that satisfy each of the following equations for £ £ 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


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