Answer:
[tex]\sec \theta=\dfrac{5}{4}.[/tex]
Step-by-step explanation:
Use the definition of secans:
[tex]\sec \theta=\dfrac{1}{\cos \theta}.[/tex]
Now you have to find the cosine of angle [tex]\theta.[/tex]
Point (12,-9) lies in fourth quadrant, then [tex]\cos \theta>0.[/tex]
Consider right triangle with legs 9 and 12, by the Pythagorean theorem,
[tex]\text{hypotenuse}^2=9^2+12^2=81+144=225,\\ \\\text{hypotenuse}=15.[/tex]
Thus,
[tex]\cos \theta=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]
and
[tex]\sec \theta=\dfrac{1}{\dfrac{4}{5}}=\dfrac{5}{4}.[/tex]
