# How do you evaluate #cos^-1(sqrt3/2)# without a calculator?

##### 1 Answer

Aug 31, 2016

30 degrees or

#### Explanation:

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