Question

the point given below is on the terminal side of (\theta). find the exact values of the six trigonometric functions of (\theta).
((-12,5))

(cos \theta = \frac{-12}{13})
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

(\tan \theta = \frac{5}{-12})
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

(cot \theta = \frac{-12}{5})
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

(sec \theta = square)
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find radius $r$

For point $(-12,5)$, $x=-12$, $y=5$. Use $r=\sqrt{x^2+y^2}$:
$$r=\sqrt{(-12)^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$$

Step2: Calculate $\sec\theta$

Use $\sec\theta=\frac{r}{x}$:
$$\sec\theta=\frac{13}{-12}=-\frac{13}{12}$$

Answer:

$-\frac{13}{12}$