Find All real numbers that satisfy the equations A cosx212 B

Solution

A.) cos(x/2)=1/2

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

x/2 = pi/3--- x = 2pi/3 , 2pi -2pi/3

x= 2k*pi + 2pi/3 , 2k*pi + 4pi/3 (General solution)

B.) cos(2x)= -rad 2

Please check what is rad 2

C.) cos(3x) =1

3x = cos^-1(1)

3x = 0

3x = 2k*pi

x = 2k*pi/3 (General solution)

D.) sin(x/3)=-1

x/3 = sin^-1(-1)

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

x= =9pi/2 +6k*pi