Question

which of the following is a solution of 2cos^2x-cost-1=0 a. 0 degrees b. 150 degrees c. 180 degrees d. 210 degrees

Answer 1

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).