Answer:
{0, 150} degrees
Step-by-step explanation:
Given 2cos^2x-cost-1=0, let's simplify this problem by temporarily replacing cos x with y:
2y^2 - y -1 = 0
This can be solved by factoring: (2y + 1)(y - 1) = 0. From this we get two solutions: y = -1/2 and y = 1.
Remembering that we let y = cos x, we now solve:
cos x = -1/2 and cos x = 1.
Note that cos x = 1 when x = 0 and the "adjacent side" coincides with the hypotenuse.
cos x = -1/2 when the hypotenuse is 2 and the "adjacent side" is -1. This has two solutions between 0 and 360 degrees: 150 degrees and 270 degrees.
Four answer choices are given. Both (a) (0 degrees) and (b) (150 degrees) satisfy the original equation. Thus, the solution set is {0, 150} (degrees).
