How do you solve Sin(3x) - sin(6x) = 0sin(3x)−sin(6x)=0?

1 Answer
Nghi N.
May 14, 2016

0, pi/3, (2pi)/3, pi/9, and (5pi)/90,π3,2π3,π9,and5π9

Explanation:

Use the trig identity: sin 2a + 2sin a.cos a.
Replace in the equation sin (6x) by 2sin (3x).cos (3x) -->
sin (3x) - 2sin (3x).cos (3x) = 0
sin (3x)(1 - 2cos 3x) = 0
a. sin 3x = 0 --> 3x = 0 and 3x = pi3x=π, and 3x = 2pi3x=2π, that give as answers-->
x = 0; x = pi/3, and x = (2pi)/3x=0;x=π3,andx=2π3
b. cos (3x) = 1/2cos(3x)=12 --> 3x = +- pi/33x=±π3 -->
x = (pi/3)/3 = pi/9x=π33=π9 and x = ((5pi)/3)/3 = (5pi)/9x=5π33=5π9
Note: the arc -(pi/3)−(π3) is co-terminal to the arc (5pi)/3.5π3.

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