Question #f2a52

1 Answer
Nghi N.
Jan 16, 2017

#x = pi/4 + kpi#
#x = (3pi)/4 + kpi#
#x = +- (2pi)/3 + 2kpi#

Explanation:

cos 2x(2cos x + 1) = 0
Either term must be zero.
a. cos 2x = 0. Unit circle gives 2 solution:
#2x = pi/2 + 2kpi#, and #2x = (3pi)/2 + 2kpi#.
#2x = pi/2 + 2kpi# --> #x = pi/4 + kpi#
#2x = (3pi)/2 + 2kpi# --> #x = (3pi)/4+ kpi#
b. 2cos x + 1 = 0
#cos x = - 1/2#
Trig table and unit circle gives -->
#cos x = - 1/2# --> #x = +- 2pi/3 + 2kpi#
General answers:
#x = pi/4 + kpi#
#x = (3pi)/4 + kpi#
#x = +- (2pi)/3 + 2kpi#

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