Find the exact value of each of the six trigonometric functions of $\theta$, if $(-4,-7)$ is a point on the terminal side of angle $\theta$.
\[
\sin \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
\[
\cos \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
\[
\tan \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
\[
\csc \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
\[
\sec \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
\[
\cot \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Step 1 ：Given the point (-4,-7) on the terminal side of angle \(\theta\), we can find the six trigonometric functions of \(\theta\) using the definitions of these functions in terms of the coordinates of the point.

Step 2 ：The x-coordinate is -4 and the y-coordinate is -7.

Step 3 ：We can find the radius using the Pythagorean theorem: \(r = \sqrt{x^2 + y^2} = \sqrt{(-4)^2 + (-7)^2} = \sqrt{65}\).

Step 4 ：The sine of \(\theta\) is the y-coordinate divided by the radius: \(\sin \theta = \frac{y}{r} = \frac{-7}{\sqrt{65}}\).

Step 5 ：The cosine of \(\theta\) is the x-coordinate divided by the radius: \(\cos \theta = \frac{x}{r} = \frac{-4}{\sqrt{65}}\).

Step 6 ：The tangent of \(\theta\) is the y-coordinate divided by the x-coordinate: \(\tan \theta = \frac{y}{x} = \frac{7}{4}\).

Step 7 ：The cosecant of \(\theta\) is the reciprocal of the sine: \(\csc \theta = \frac{1}{\sin \theta} = \frac{-\sqrt{65}}{7}\).

Step 8 ：The secant of \(\theta\) is the reciprocal of the cosine: \(\sec \theta = \frac{1}{\cos \theta} = \frac{-\sqrt{65}}{4}\).

Step 9 ：The cotangent of \(\theta\) is the reciprocal of the tangent: \(\cot \theta = \frac{1}{\tan \theta} = \frac{4}{7}\).

Step 10 ：Final Answer: \(\boxed{\sin \theta = \frac{-7}{\sqrt{65}}, \cos \theta = \frac{-4}{\sqrt{65}}, \tan \theta = \frac{7}{4}, \csc \theta = \frac{-\sqrt{65}}{7}, \sec \theta = \frac{-\sqrt{65}}{4}, \cot \theta = \frac{4}{7}}\)