Question

How do you solve for x in `sin(x) = sin(2x)` where x is between [0,360]?

Answer 1

`x epsilon {0^o, 60^o, 180^o, 330^o}`

`sin(x) = sin(2x)`
By double angle formula:
`sin(x) = 2 * sin(x) * cos(x)`
`sin(x) = 0` or `1 = 2 * cos(x)`

If `sin(x) = 0`
then `x = 0^O or 180^o`

If `1 = 2 * cos(x)`
then `cos(x) = 1/2`
`rarr` `x = 60^o or 330^O`