Solve the equation over the interval 02pi Cos2x square root

Solve the equation over the interval [0,2pi]. Cos(2x) = square root 3/2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. X = (Type exact answers in terms of pi. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed.) There is no solution.

Solution

cos(2x) = 3 /2 ; interval is [0 , 2)

==> 2x = cos^-1 (3 /2)

==> 2x = /6 , 2 - /6 , 2 + /6 , 4 - /6 (since cosine function is positive in 1^st and 4^th quadrants)

==> 2x = /6 , 11/6 , 13/6 , 23/6

==> x = /12 , 11/12 , 13/12 , 23/12

Hence x = /12 , 11/12 , 13/12 , 23/12