solve the equation on the interval 0

solve the equation on the interval 0<_<2
sec(3\\2)=-2

This Question: 1 pt Solve the equation ontheiteraros0

Solution

sec(3x/2) = -2

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

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

3x/2 = 2k*pi +2pi/3

x = ( 4pi +12k*pi)/9

3x/2 = 2k*pi +4pi/3

x = (8pi +12k*pi)/9

Plug k= 0, 1, 2....

x = 4pi/9 , 8pi/9 , 16pi/9   ; 0<=x<= 2pi