arccos(1/2) Evaluate the expression without using a calculator

arccos(1/2)
Let this expression be equal to y.
y = arccos(1/2)
Rewriting this in terms of cosine function the equation becomes:
cos(y) =1/2
Base on the Unit Circle Chart, cosine is 1/2 at angles pi/3 and (5pi)/3.
y=pi/3, (5pi)/3
Then, consider the original equation again.
y = arccos(1/2)
Take note that the range of arccosine is 0lt=ylt=pi . Between pi/3 and (5pi)/3 , it is only pi/3 that belongs to this interval. So the solution to the original equation is:
y = arccos(1/2)
y=pi/3
 
Therefore, arccos(1/2) = pi/3 .