Find all solutions on the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to four decimal places. If an answer does not exist, enter DNE.)

Question

12sin²(t) + cos(t) - 3 = 3

Answer 1

12sin²(t) + cos(t) - 3 = 3

12(1-cos²(t)) + cos(t) - 6 = 0

12Cos²(t) - cos(t) - 6 = 0

(4cos(t) - 3)(3cos(t) + 2) = 0

cos(t) = 3/4 cos(t) = -2/3

arccos(3/4) =41.41° acrcos(-2/3) = 131.8°