Grade 11 Trigonometry Question

Let's say I am given an angle of (5*pie)/6.

P((5*pie/6)) = (x, y). I know that for x I do cos of the angle and for y, I do sin of the angle but, what I do not know how to do is to get a NON-DECIMAL answer. My teacher gave me some paper with questions that tells me to NOT use a calculator.

For example for the x coordinate:

In radians:

cos ((5*pie)/6) ~ -0.87 (an approximate answer)...how do I know that I need to get -(sqrt(3)/2) instead? Do I HAVE to memorize this kind of thing or is there a method to solve this?