I don't understand the logic behind how to find x in the equation: cos (x)= 1/2

(how do you find it on the calculator?)

Well, you already have the cos(x) = 1/2, so all you have to do is take the "inverse cos of 1/2", which will give you:

60-degree angle.

P.S. The "inverse cos" on the calculator here is written as "acos", which is the same thing as inverse cos.