Question

How do you find `cos( cot^{-1} sqrt{3} )` without a calculator?

Answer 1

Below

Explanation:

`cot^(-1)sqrt3 = 1/tan^(-1)sqrt3 = 1/60`

Since `1/60` is approximately equal to `0.010` and looking at the `y=cosx` graph below,

graph{cosx [-10, 10, -5, 5]}

We can give an approximation that `cos (1/60)=1`