Question

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

Answer 1

`((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}`