How do you solve for the exact solutions in the interval [0,2pi] of sin 2x - sin x= 0?

1 Answer
Nghi N.
Apr 16, 2016

0, pi/3, pi, (5pi)/3, 2pi

Explanation:

Apply the trig identity: sin 2a = 2sin a.cos a. WE get:
2sin x.cos x - sin x = 0
sin x(2cos x - 1) = 0
a. sin x = 0 --> x = 0 , x = pi, x = 2pi
b. 2cos x = 1 --> cos x = 1/2 ---> x = = +- pi/3
The co-terminal arc of (-pi/3) is (5pi)/3
Answers for (0, 2pi):
0, pi/3, pi, (5pi)/3, 2pi

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