# How do you find the exact value of cot^-1(cot((2pi)/3))?

Jun 21, 2017

${\cot}^{-} 1 \left(\cot \left(\frac{2 \pi}{3}\right)\right) = \left(\frac{2 \pi}{3}\right)$

#### Explanation:

Let ${\cot}^{-} 1 \left(\cot \left(\frac{2 \pi}{3}\right)\right) = \theta$ , then

$\cot \theta = \cot \left(\frac{2 \pi}{3}\right) \therefore \theta = \left(\frac{2 \pi}{3}\right) \therefore$

${\cot}^{-} 1 \left(\cot \left(\frac{2 \pi}{3}\right)\right) = \left(\frac{2 \pi}{3}\right)$ [Ans]

Jun 21, 2017

Assuming $\textcolor{b l u e}{{\cot}^{-} 1}$ is defined as a function with a range of $\textcolor{b l u e}{\left[0 , \pi\right)}$
then ${\cot}^{-} 1 \left(\cot \left(\frac{2 \pi}{3}\right)\right) = \textcolor{red}{\frac{2 \pi}{3}}$