Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2𝜋).

Question

Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2𝜋). (Enter your answers as a comma-separated list. Round each answer to four decimal places.)

4 cos²(x) − 4 cos(x) − 1 = 0 

x=

Answer 1

cos(x) = (4±√(16-(4)(4)(-1))/(2(4))

The range of cos(x) is [-1, 1], so take the value less than one because the other value doesn't make sense.

x = cos^-1(cos(x))

You should get an answer for both the second and third quadrants.