How do you evaluate tan1(33) without a calculator?

1 Answer
Sep 29, 2016

tan1(33)=π6

Explanation:

Consider a triangle with sides in ratio 1:3:2

This is a right angled triangle since:

12+32=1+3=4=22

In fact, it is one half of an equilateral triangle, hence has angles π6, π3, π2...

enter image source here

Now tan(θ)=oppositeadjacent

Hence we find:

tan(π6)=13=33

Since π6 radians is in Q1, this is the value of tan1(33)