Respuesta :
Explanation
Given the following information:
[tex]\begin{gathered} Sin=\frac{-3}{5} \\ Cos>0 \end{gathered}[/tex]This implies that the value of sin is negative while that of cos is positive.
This occurs in the fourth quadrant. This also means that the value of tan is negative.
We know that sin uses the value of the opposite and the hypotenuse.
We need to determine the value of the adjacent.
[tex]\begin{gathered} Adjacent=\sqrt{Hyp^2-Opp^2} \\ where \\ Hyp=5 \\ Opp=3 \end{gathered}[/tex][tex]\begin{gathered} Adjacent=\sqrt{5^2-3^2}=\sqrt{25-9}=\sqrt{16} \\ Adj=4 \end{gathered}[/tex]We know that cot is the reciprocal of tan. The value of tan is given as:
[tex]\begin{gathered} Tan=\frac{Opp}{Adj}=\frac{3}{4} \\ But\text{ tan is negative in the fourth quadrant. } \\ \therefore Tan=\frac{-3}{4} \end{gathered}[/tex]We can now determine the value of cot to be:
[tex]Cot=\frac{-4}{3}(reciprocal\text{ of tan\rparen}[/tex]Hence, the answer is the second option i.e. -4/3.
