The values of $\sin \theta$ and $\cos \theta$ are given below. Find the exact value of each of the four remaining trigonometric functions.
\[
\sin \theta=\frac{3 \sqrt{10}}{10}, \cos \theta=-\frac{\sqrt{10}}{10}
\]
\[
\tan \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\cot \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\csc \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\sec \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Step 1 ：Given that \(\sin \theta = \frac{3 \sqrt{10}}{10}\) and \(\cos \theta = -\frac{\sqrt{10}}{10}\)

Step 2 ：We can calculate the other trigonometric functions using these values.

Step 3 ：The tangent of an angle is the sine of the angle divided by the cosine of the angle, so \(\tan \theta = \frac{\sin \theta}{\cos \theta} = -3\)

Step 4 ：The cotangent is the reciprocal of the tangent, so \(\cot \theta = \frac{1}{\tan \theta} = -\frac{1}{3}\)

Step 5 ：The cosecant is the reciprocal of the sine, so \(\csc \theta = \frac{1}{\sin \theta} = \frac{\sqrt{10}}{3}\)

Step 6 ：The secant is the reciprocal of the cosine, so \(\sec \theta = \frac{1}{\cos \theta} = -\sqrt{10}\)

Step 7 ：Final Answer: \(\tan \theta = \boxed{-3}\), \(\cot \theta = \boxed{-\frac{1}{3}}\), \(\csc \theta = \boxed{\frac{\sqrt{10}}{3}}\), \(\sec \theta = \boxed{-\sqrt{10}}\)