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

-3/4
3/4
4/3
-4/3

User Mattias
by
7.8k points

1 Answer

4 votes
ANSWER


\cot( \theta) = - (4)/(3)


Step-by-step explanation

We were given that


\sin( \theta) = - (3)/(5)

We need to find

\cot( \theta) .

We know that,


\cot( \theta) = ( \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 + {( ( - 3)/(5) )}^(2) = 1




\cos^(2) \theta + (9)/(25) = 1



\cos^(2) \theta = 1 - (9)/(25)


\cos^(2) \theta = (16)/(25)





\cos\theta = \pm \: \sqrt{ (16)/(25) }



\cos\theta = \pm \: (4)/(5)

Since we are dealing with the fourth quadrant,


\cos\theta = (4)/(5)


This implies that,



\cot( \theta) = ( (4)/(5) )/( - (3)/(5) )


\cot( \theta) = - (4)/(3)

The correct answer is D.
User Stephan Du Toit
by
8.1k points

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