Solve the equation on the interval 0 ≤ θ < 2π. 2 cos θ + 1 = 0

Answer 1

2cosx + 1 = 0

2cosx =-1

cosx =-1/2

x = 2pi/3 or 4pi/3 radians

theta = 120 degrees or 240 degrees

reference angle is pi/3 or 60 degrees. It forms a right triangle with adjacent side = -1, opposite side = sqr3 and hypotenuse = 2. cosx = adjacent side over hypotenuse. cosines are negative only in quadrants II and III.

theta = 180 -60 or 180+60 = 120 or 240 degrees

2pi/3 = 120, 4pi/3 = 240