Question

Use the inverse functions to find all solutions in the interval `[0, 2π)` `3cos^2(x) + 5cos(x) = 0`?

Answer 1

`pi/2` and `(3pi)/2`

Explanation:

We can factorise this equation to get:
`cos(x)(3cos(x)+5)=0`

`cosx=0 or cosx=-5/3`

`x=cos^-1(0)=pi/2,2pi-pi/2;pi/2,(3pi)/2`
or
`x=cos^-1(-5/3)="undefined"`, `abs(cos^-1(x))<=1`

So, the only solutions are `pi/2` and `(3pi)/2`