Question

What are the two solutions of cos(x/2)=−2/2?

(a) x = 120° and x = 240°
(b) x = 150° and x = 330°
(c) x = 180° and x = 360°
(d) x = 210° and x = 450°

Answer 1

The two solutions to the equation cos(x/2) = -2/2 are x = 180° + 360°(n) and x = -180° + 360°(n), where n is an integer.

Step-by-step explanation:

The solution to the equation cos(x/2) = -2/2 is given by multiplying both sides by 2, which gives cos(x/2) = -1. Then we can find the reference angle by taking the inverse cosine of -1, which is 180°. Since cosine is negative in the second and third quadrants, we can find the two solutions by adding and subtracting the reference angle from multiples of 360°.

Therefore, the two solutions are x = 180° + 360°(n) and x = 180° - 360°(n), where n is an integer. Simplifying these solutions, we get x = 180° + 360°n and x = -180° + 360°n.

Plug in integers for n to find the specific values of x that satisfy the equation.