Question

solve the equation if 0 degrees is less than or equal to x which is less than or equal to 360 degrees. cos x= -1/2

Answer 1

x = {120°, 240°}

Explanation:

cos x = -1/2 for 0 ≤ x ≤ 360°

That cosine of x = -1/2 tells us two things immediately: 1) the hypotenuse has length 2 and the side adjacent to the angle x is -1. To have a negative adjacent side, angle x must be in either Quadrant II or Quadrant III.

If in Quadrant II, the terminal side of angle x is 30° past 90°, which means that x = 120°. If in Quadrant III, the terminal side of x is 30° short of 270°, which means that x = 240°

Then x = {120°, 240°}