What are all solutions of equation cos x=-0.5, in the set [0,2pi)? (Provide the answer in radians).

Expert Answers
justaguide eNotes educator| Certified Educator

The equation to be solved for values of x in the interval [0, 2*pi] is : cos x = -0.5

x = arc cos (-0.5)

x = 2*pi/3

and x = 4*pi/3

The required solutions for cos x = -0.5 are (2*pi/3 , 4*pi/3)

giorgiana1976 | Student

We'll have to determine all possible values for x, located in the interval [0,2pi), that makes the value of cosine function -0.5.

We'll write the values -0.5 = -1/2

The cosine function is negative in the 2nd and the 3rd quadrants.

x = arccos(-1/2)

x = pi - pi/3

x = 2pi/3 (2nd quadrant)

x = pi + pi/3

x = 4pi/3 (3rd quadrant)

The possible values for x, in radians, located in the set [0,2pi), are: {2pi/3; 4pi/3}.