Find the solutions of the equation that are in the interval [0, 2𝜋). (If there is no solution, enter NO SOLUTION.)

Question

Find the solutions of the equation that are in the interval [0, 2𝜋). (If there is no solution, enter NO SOLUTION.)

4 cos² 𝛾 + 2 cos 𝛾 = 0



Answer 1

4cos^2(x) +2cos(x) =0. Factor out 2cos(x)

2cos(x)[2cos(x) +1) ] =0

2cos(x)=0 x= pi/2 and 3pi/2

2cos(x) +1= 0

cos(x) = -1/2. x= 3pi/4 and 5/pi/4