Answer:
[tex]\sec \theta = -\frac{\sqrt{61}}{5}[/tex]
Step-by-step explanation:
The secant can be found by the following trigonometric relation:
[tex]\sec \theta = \frac{1}{\cos \theta}[/tex]
[tex]\sec \theta = \frac{1}{\frac{x}{r} }[/tex]
[tex]\sec \theta = \frac{r}{x}[/tex]
[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]
[tex]\sec \theta = \frac{\sqrt{(-5)^{2}+(-6)^{2}}}{(-5)}[/tex]
[tex]\sec \theta = -\frac{\sqrt{61}}{5}[/tex]
