How do i solve 1=2cos(3x-5pi) for [0,2)?

1=2cos(3x-5pi) for [0,2pi)?

1 Answer
Nghi N
Feb 14, 2018

x = +- (2pi)/9, or
x = +- 40^@

Explanation:

cos (3x - 5pi) = 1/2
cos (3x - 5pi) = cos (3x - pi) = - cos 3x -->
cos 3x = - 1/2
Trig table and unit circle give 2 solutions:
3x = +- (2pi)/3
x = +- (2pi)/9
Check by calculator:
x = (2pi)/9 = 40^@ --> 2cos (3x - pi) = 2cos (120 - 180) =
= 2cos (-60) = 2cos 60 = 2(1/2) = 1 Proved.

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