Question

How do you solve `sqrt(3) - 2Sin(6x) = 0` from `[0,2pi]`?

Answer 1

`sqrt(3)-2sin(6x)=0` with `x epsilon [0,2pi]`
`rarr` `color(white)("XXXX")` `x = pi/9 or pi/18`

Explanation:

Temporarily replace `6x` with `theta`

`sqrt(3) - 2sin(theta) = 0`

`rarr` `color(white)("XXXX")` `sin( theta) = sqrt(3)/2`

within the range `[0,2pi]` this is one of the standard angles with
`color(white)("XXXX")` `theta = pi/3` or `theta= (2pi)/3`

Since `theta = 6x`
`color(white)("XXXX")` `6x = pi/3` or `6x = (2pi)/3`

`rarr` `color(white)("XXXX")` `x = pi/18` or `x = pi/9`