Solve the equation Give a general formula for all the soluti

Solve the equation. Give a general formula for all the solutions. List all the solutions for k equals=0, 1, and 2. cos=square root of 2 over 2 Write the general form for all the solutions to cos=square root of 2 over 2 based on the smaller angle.

Solution

cos =sqrt(2)/2

= cos^-1(sqrt2/2)

= pi/4 , 2pi -pi/4

= pi/4 , 7pi/4

Based on smaller angle general form solution :

= 2k*pi + pi/4

= ( 8k*pi +pi)/4

k =0 ; = pi/4

k = 1 ; = 9pi/4

k=2 ; = 17pi/4