Question #00e9a

1 Answer
Nghi N.
Aug 16, 2016

0; pi/3; (2pi)/3; and (4pi)/3

Explanation:

Apply the trig identity:
sin a + sin b = 2sin ((a +b)/2)cos ((a - b)/2)
sin 2x + sin 4x = 2sin ((6x)/2)cos ((2x)/2) = 2sin 3x.cos x
(sin 2x + sin 4x) + sin 3x = sin 3x(2cos x + 1) = 0
Either one of the 2 factors must be zero.
a. sin 3x = 0 .
Trig table give 3 solution arcs:
3x = 0 --> x = 0
3x = pi --> x = pi/3
3x = 2pi --> x = (2pi)/3
b. 2cos x + 1 = 0 --> cos x = - 1/2
Trig table and unit circle give 2 solution arcs:
x = 2pi/3 and x = - (2pi)/3 --> or x = (4pi)/3 (co-terminal)
Answers for (0, 2pi):
0, pi/3, (2pi)/3, (4pi/3)

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