Answer
$tan\theta=-\frac{1}{3}, cot\theta=-3, sec\theta=\frac{\sqrt {10}}{3}, csc\theta=-\sqrt {10}$
Work Step by Step
Step 1. Based on the given values, we can identify that $\theta$ is in quadrant IV.
Step 2. Form a right triangle with sides $x=3\sqrt {10}, y=\sqrt {10}, r=10$ with $|\theta|$ facing $y$.
Step 3. We can find $tan\theta=-\frac{1}{3}, cot\theta=-3$
Step 4. We can find $sec\theta=\frac{\sqrt {10}}{3}, csc\theta=-\sqrt {10}$
