Question

what is the value of cot 660 degrees?

Answer 1

$cot660°$

$$\begin{gathered} =cot\left(360°+300°\right) \\ =cot300° \end{gathered}$$

We know that $cot\left(180°-x\right)=-cotx$

So, $cot660°$

$$\begin{gathered} =cot300° \\ =cot\left(180°-\left(-120\right)\right) \end{gathered}$$

$$\begin{gathered} =-cot\left(-120°\right) \\ =cot120° \end{gathered}$$

$$\begin{gathered} =cot\left(180°-60°\right) \\ =-cot60° \end{gathered}$$

$=-\frac{1}{\sqrt{3}}$