Question

How do you use inverse trig functions to solve equations?

Answer 1

`sinx=n` if and only if `x=arcsinn + 2 pi k` for some integer `k`

or `x=(pi-arcsinn) + 2 pi k` for some integer `k`

`cosx=n` if and only if `x=arccosn + 2 pi k` for some integer `k`

or `x=(pi+arccosn) + 2 pi k` for some integer `k`

`tanx=n` if and only if `x=arctan n + pi k` for some integer `k`

and so on.

So,: Solve `7sinx-5 = 0`

`7sinx-5 = 0`
`7sinx = 5`
`sinx = 5/7`

`x=arcsin(5/7) +2 pi k` for integer `k`
or `(pi-arcsin(5/7)) +2 pi k` for integer `k`