Question

Solve the following equation; domain 0< x < 360; 3 cot x + sqrt 3 = 0

< is less than or equal too (I don't have the symbol on my keyboard. )
sqrt = square root.

Answer 1

ANSWER


`x =120 \degree \: or \: 300 \degree`

Step-by-step explanation

We want to solve the trigonometric equation


`3 \cot(x) + √(3) = 0`

We group like terms to obtain,


`3\cot(x) = - √(3)`

Divide both sides of the equation by 3 to get,


`\cot(x) = - ( √(3) )/(3)`

We can reciprocate both sides to get,


`\tan(x) = - (3)/( √(3) )`

We simplify the right hand side to get,


`\tan(x) = - √(3)`

Since the tangent ratio is negative, it implies that it is either in the second quadrant or fourth quadrant.

In the second quadrant,


`x = 180 \degree - arctan( √(3))`


`x = 180 \degree - 60 \degree = 120 \degree`

In the fourth quadrant,


`x = 360 \degree - arctan( √(3))`


`x = 360 \degree - 60 \degree`


`x = 300 \degree`