Question

Can someone please solve this problem

Answer 1

ANSWER

$\boxed { \sqrt{} }30 \degree$

$\boxed { \sqrt{} }210 \degree$

EXPLANATION

We want to solve

$\cot( \theta) = \sqrt{3}$

where

$0 \degree \: \leqslant x \leqslant 360 \degree$

We reciprocate both sides of this trigonometric equation to obtain:

$\tan( \theta) = \frac{1}{ \sqrt{3} }$

We take arctangent of both sides to get;

$\theta = \tan ^{ - 1} ( \frac{1}{ \sqrt{3} } )$

$\theta = 30 \degree$

This is the principal solution.

The tangent ratio is also positive in the third quadrant.

The solution in the third quadrant is

$180 + \theta = 180 + 30 = 210 \degree$