Find the solutions of the equation that are in the interval

Find the solutions of the equation that are in the interval [0, 2pi). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) cos (2x - pi/5) = 0

Solution

cos(2x - pi/5)=0

(2x - pi/5 ) =pi/2

2x = pi/5 +pi/2

2x = 7pi/10 +2k*pi

x = 7pi/20 + k*pi

k =0 ; x = 7pi/20

k =1 ; x = 7pi/20 +pi = 27pi/20

(2x - pi/5 ) = 3pi/2

2x = pi/5 +3pi/2

2x = 17pi/10 +2kpi

x = 17pi20 + kpi

k =0 ; x = 17pi/20

k =1 ; x = 17pi/20 +pi = 37pi/20

Solution in the interval [ 0, 2pi ) : x= 7pi/20 , 27pi/20 , 17pi/20 , 37pi/20