find the solutions of the equation that arein the interval [0.pi). cos(1/4 x) = -1/2

Answer 1

Given the interval you are working with and the fact that the cosine value is negative, you are looking at a 2nd quadrant angle. Since it's cosine ratio is -1/2, the reference angle would have to be 120º or 2π/3 radians. To solve for x, we set the actual angle measure of 2π/3 radians equal to the expression 1/(4x) and then solve the equation:

2π/3 = 1/(4 x) → 8πx = 3 →x = 3/(8π). Now if we check this in both the given interval for the angle and in the original equation and take its cosine value, the value for x checks on both counts.