Question #e3529

2 Answers
Mar 12, 2017

#x = pm 2/3 k pi# for #k =0,1,2,cdots#

Explanation:

#sin(2x)=-sinx = sin(-x)# then

#2x=-xpm 2kpi# and

#x = pm 2/3 k pi# for #k =0,1,2,cdots#

Mar 12, 2017

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

Explanation:

sin x + 2sin 2x = 0
sin x + 2sin x.cos x = 0
sin x(1 + 2cos x) = 0
a. sin x = 0 --> unit circle gives 3 solutions -->
x = 0, #x= pi#, and #x = 2pi#
b. 1 + 2cos x = 0
#cos x = - 1/2#
Trig table of special arcs and unit circle give -->
#x = +- (2pi)/3#
General answers
#x = kpi#, and
#x = +- (2pi)/3 + 2kpi#