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

##### 1 Answer
Aug 31, 2016

30 degrees or $\frac{1}{6} \pi$

#### 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 $\sqrt{3}$

From this triangle tan 60 =$\sqrt{3}$, cos 60 =$\frac{1}{2}$, sin 60=$\frac{\sqrt{3}}{2}$
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