Solve the equation for x if 0 ≤ x < 2𝜋. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.) 4 sin2 x + 4 cos x − 5 = 0

Answer 1

4sin^2x + 4cosx - 5 = 0

4(1-cos^2x) + 4cosx -5 = 0

4 - 4cos^2x + 4cosx - 5 = 0

4cos^2x - 4cosx + 1 = 0

6

cosx = 4/8 + or - (1/8)sqr(16 -16)

cosx = 1/2

x = 60 degrees = pi/3 radians or 300 degrees = 5pi/3 radians

x = pi/3, 5pi/3

4sin^2x + 4cosx = 5, cosx= 1/2, sinx = sqr3/2

4(3/4) + 4(1/2) + 5 = 0

3 + 2 =5

Answer 2

4 sin² x + 4 cos x = 5

4(1 - cos² x) + 4 cos x - 5 = 0

Simplify and use zero product rule from Algebra 2.