Question

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

Answer 1

`0, pi/3, (2pi)/3, pi/9, and (5pi)/9`

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 = pi`, and `3x = 2pi`, that give as answers-->
`x = 0; x = pi/3, and x = (2pi)/3`
b. `cos (3x) = 1/2` --> `3x = +- pi/3` -->
`x = (pi/3)/3 = pi/9` and `x = ((5pi)/3)/3 = (5pi)/9`
Note: the arc `-(pi/3)` is co-terminal to the arc `(5pi)/3.`