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

1 Answer
Aug 31, 2016

Answer:

30 degrees or #1/6pi#

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 #sqrt3#

From this triangle tan 60 =#sqrt3#, cos 60 =#1/2#, sin 60=#sqrt3/2#
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