Question

How do you solve `sin 3x = 0`?

Answer 1

sin 3x = 0
`a. sin 3x = 0 = sin 0 -> x = 0`
`b. sin 3x = 0 = sin pi -> 3x = pi -> x = pi/3`
`c. sin 3x = 0 = sin 2pi -> 3x = 2pi-> x = (2pi)/3`

Answer 2

Solve sin 3x = 0.

Explanation:

There is another way to solve sin 3x = 0.
Use the trig identity: `sin 3x = 3sin x - 4sin^3 x`
`sin 3x = sin x(3 - 4sin^2 x)`

a. sin x = 0 --> x = 0, and `x = pi`, and `x = 2pi.`
b. `(3 - 4sin^2 x) = 0`
`4sin^2 x = 3`
`sin^2 x = 3/4` --> `sin x = +- sqrt3/2`
- When `sin x = sqrt3/2` --> `x = pi/3` and `x = 2pi/3`
- When `sin x = -sqrt3/2` --> `x = - pi/3` and `x = -2pi/3.`

Answer 3

`sin 3x=0`

`sin 3x=sin kpi, k in ZZ`

`3x= kpi, k in ZZ`

`x= (kpi)/3, k in ZZ`

Answer 4

`x=0`

Explanation:

We start by taking the inverse sine (`arcsin`) of both sides. Arcsin cancels with `sin` and we get:

`3x=arcsin(0)`

`3x=0`

`x=0`