2 years ago

Magmatic and English

Mathematics

1 answer:

kozerog [31]2 years ago

7 0

I don’t really get that sorry I would love to help but don’t know what that mean.

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

kondaur [170]

ANSWER

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

EXPLANATION

We want to solve the trigonometric equation

$3 \cot(x) + \sqrt{3} = 0$

We group like terms to obtain,

$3\cot(x) = - \sqrt{3}$

Divide both sides of the equation by 3 to get,

$\cot(x) = - \frac{ \sqrt{3} }{3}$

We can reciprocate both sides to get,

$\tan(x) = - \frac{3}{ \sqrt{3} }$

We simplify the right hand side to get,

$\tan(x) = - \sqrt{3}$

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

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$x = 180 \degree - arctan( \sqrt{3})$

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

In the fourth quadrant,

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$x = 360 \degree - 60 \degree$

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