`2cos^2 (x) + 7sin(x) = 5` Use inverse functions where needed to find all solutions of the equation in the interval `0,2pi)`.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

First transform `cos^2(x)` into `1-sin^2(x)` :



This is a quadratic equation for sin(x), the roots are

sin(x)=3 and sin(x)=1/2.

The first is impossible, the second has two roots on `(0, 2pi)`, `pi/6` and `(5pi)/6.`