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

2π/3, 4π/3

Step-by-step 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°)

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: