Determine the specific solutions if any to the equation on t

Determine the specific solutions (if any) to the equation on the interval [0.2 cos 20-6 sin 205 What are the solutions to the equation cos 20-6 sin20 -5 on the interval (0.2x)? Select the correct choice below and il in any answer boxes within your choice. O A. The solutions are 0 B. There are no solutions in the interval [02 (Simplify your answer Type an exact answer using as needed. Use a comma to separate answers as needed.)

Solution

cos(2 theta) - 6sin²theta=-5

1-2sin²theta -6 sin²theta=-5

6-8 sin²theta=0

sin²theta=3/4

sin theta=+-sqrt(3)/2

theta= pi/3, 2pi/3, 4pi/3,5pi/3