Question

If sin Θ=-3/5 and the angle is in quadrant IV, what is cot Θ?

Answer 1

ANSWER

$\cot( \theta) = - \frac{4}{3}$


EXPLANATION

We were given that

$\sin( \theta) = - \frac{3}{5}$

We need to find
$\cot( \theta) .$

We know that,

$\cot( \theta) = \frac{ \cos( \theta) }{ \sin( \theta) }$


We now need to find
$\cos( \theta)$

using the Pythagorean identity or the right angle triangle.

According to the Pythagorean identity,

$\cos^{2} \theta + \sin^{2} \theta = 1$


$\cos^{2} \theta + {( \frac{ - 3}{5} )}^{2} = 1$



$\cos^{2} \theta + \frac{9}{25} = 1$


$\cos^{2} \theta = 1 - \frac{9}{25}$

$\cos^{2} \theta = \frac{16}{25}$




$\cos\theta = \pm \: \sqrt{ \frac{16}{25} }$


$\cos\theta = \pm \: \frac{4}{5}$

Since we are dealing with the fourth quadrant,

$\cos\theta = \frac{4}{5}$


This implies that,


$\cot( \theta) = \frac{ \frac{4}{5} }{ - \frac{3}{5} }$

$\cot( \theta) = - \frac{4}{3}$

The correct answer is D.