Question

Find the value of $\cot {240}^{\circ }$

• A. $-\frac{1}{\sqrt{3}}$
• B. $\frac{1}{\sqrt{3}}$
• C. $-\sqrt{3}$
• D. $\sqrt{3}$

Answer 1

The correct option is B $\frac{1}{\sqrt{3}}$

We have,
$\cot {240}^{\circ }=\cot ({180}^{\circ }+{60}^{\circ })$
$({180}^{\circ }+{60}^{\circ })$ lies in 3rd quadrant.
We know that $\cot ({180}^{\circ }+\theta )=\cot \theta$
$\therefore \cot ({180}^{\circ }+{60}^{\circ })=\cot {60}^{\circ }=\frac{1}{\sqrt{3}}$