Question

How do you solve `sin(x + 40) = 0.7` where 0<x<360?

Answer 1

The value `0.7` is not one of the remarkable values of the function sinus, so:

`sin(x+40°)=0.7rArr`

`x+40°=arcsin0.7+k360°rArr`

`x=-40°+arcsin0.7+k360°`

and

`x+40°=180°-arcsin0.7+k360°rArr`

`x=140°-arcsin0.7+k360°`.

This is because an equation in the variable sinus, when it has solutions, it has supplementary solutions.