How do you evaluate #cos^-1(sqrt3/2)# without a calculator?
30 degrees or
If you draw an equilateral triangle and cut it in half the ratio of the hypotenuse and the shorter other side are 2:1 Pythagoras gives us the third side as
From this triangle tan 60 =
And in the same what you have the exact values for sin , cos and tan of 30.
The other triangle which is useful is the isosceles right angle triangle whic gives exact ratios for sin cos and tan of 45 degrees