Name two angles, one between 0 and 2π, and another between 2π and 4π, that have the same cosine as pi/3

Answer 1

cos (pi/3) = cos(60) = 1/2

cosine is positive in quadrants 1 and 4

quadrant 4: 360-60 degrees = 300 degrees = (300/180)*pi = 5*pi/3

so in [0, 2*pi) the angle of interest is 5*pi/3 = 300

in (2*pi,4*pi) they are pi/3 + 2*pi = pi/3 + 6*pi/3 = 7*pi/3

5*pi/3 + 2*pi = (5/3)*pi + (6/3)*pi = (11/3)*pi

Answer 2

5π/3; 7π/3, 11π/3