Question #d5864

1 Answer
Nghi N
May 19, 2017

pi/8; (3pi)/8; (5pi)/8; (7pi)/8; (9pi)/8; (11pi)/8; (13pi)/8; (15pi)/8

Explanation:

cos 4x = 0
The unit circle gives 2 solutions:
#4x = pi/2#, and #4x = (3pi)/2#.
a. #4x = pi/2 + 2kpi#
#x = pi/8 + (kpi)/2#
b. #4x = (3pi)/2 + 2kpi#
#x = (3pi)/8 + (kpi)/2#
8 answers for #[0, 2pi]# --> k = 0, 1, 2, 3,
k = 0 --> #x = pi/8#;
k = 1 --> #x = pi/8 + pi/2 = (5pi)/8#;
k = 2 --> #x = pi/8 + pi = (9pi)/8#,
k = 3 --> #x = pi/8 + (3pi)/2 = (13pi)/8#
k = 0 --> #x = (3pi)/8#;
k = 1 --> #x = (3pi)/8 + pi/2 = (7pi)/8#
k = 2 --> #x = (3pi)/8 + pi = (11pi)/8#;
k = 3 --> #x = (3pi)/8 + (3pi)/2 = (15pi)/8#

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