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kow [346]
3 years ago
5

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

Mathematics
1 answer:
viva [34]3 years ago
8 0
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.
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