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Type the correct answer in each box. use numerals instead of words if neasary

Type the correct answer in each box. use numerals instead of words if neasary-example-1

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((5)/(13),y)

This is given point in the fourth quadrant.

In this point, the adjacent is


(5)/(13)

The opposite is y.

Find hypotenuse h using the pythagorean theorem:


\begin{gathered} h^2=((5)/(13))^2+y^2 \\ h=\sqrt[]{(25)/(169)+y^2} \end{gathered}
\sec (\theta)

is equal to hypotenuse by adjacent.


\cot (\theta)

is equal to adjacent by opposite.

In the fourth quadrant,


\sec \theta

is positive , and


\cot \theta

is negative.

So,


\begin{gathered} \sec \theta=(h)/((5)/(13)) \\ =\frac{13\sqrt[]{(25)/(169)+y^2}}{5} \\ \cot \theta=((5)/(13))/(-y) \\ =-(5)/(13y) \end{gathered}

User Gimel
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