Question

3) Solve for x: cos(x) = 1/2
a) pi/3 and 5pi/3
b) pi/3 + k(pi) and 5pi/3 + k(pi)
b) pi/3 + 2k(pi) and 5pi/3 + 2k(pi)
b) pi/3 + 1/2k(pi) and 5pi/3 + 1/2k(pi)

Is there a way of checking for this without using a calculator to eliminate the incorrect ones?

Answer 1

Firstly you know that you want more than two values, so something with a 'k' in eliminating a. Also the period of cos is 2pi, so everytime you add on 2pi you get the same answer, so you want pi/3 +2k(pi).