Question

Solve the equation 2 cos ( x ) + 1 = 0 2 cos x + 1 = 0 , 0 ≤ x ≤ 2 π 0 ≤ x ≤ 2 π . Show all of your work

Answer 1

2π/3, 4π/3

Explanation:

I interpret your question as asking us to solve the equation

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -½x

x = arccos(-½), 0 ≤ x ≤2π

Since the cosine is negative, x must be in the second or third quadrant.

Referring to the unit circle, we find that

x = 2π/3 (120°) or x = 4π/3 (240°)