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

Jun 14, 2018

Below

#### Explanation:

${\cot}^{- 1} \sqrt{3} = \frac{1}{\tan} ^ \left(- 1\right) \sqrt{3} = \frac{1}{60}$

Since $\frac{1}{60}$ is approximately equal to $0.010$ and looking at the $y = \cos x$ graph below,

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

We can give an approximation that $\cos \left(\frac{1}{60}\right) = 1$