Question

How do you solve for the exact solutions in the interval [0,2pi] of `2cos^2 (x) +5cos (x) + 2=0`?

Answer 1

This a quadratic in cos(x). The roots are cos(x) = -. 1/2 and -2. -2 is less than -1, and so, inadmissible, The only solution in`[0, 2pi]` is x = `arccos(-1/2)` = 120 deg.