2. Solve $\cot \theta=-\frac{1}{6}$ for $\frac{3 \pi}{2}< \theta< 2 \pi$.
Approximate your answer to 4 decimal places. Solve it without using a right triangle (use calculator and show what you entered in your calculator).
Answer
Final Answer: The solution to the equation \(\cot \theta=-\frac{1}{6}\) for \(\frac{3 \pi}{2}<\theta<2 \pi\) is \(\boxed{8.0191}\) radians
Step 1 ：Rewrite the equation as \(\tan \theta=-6\)
Step 2 ：Use the arctan function to find the angle whose tangent is -6
Step 3 ：Since the arctan function returns a value in the interval \(-\frac{\pi}{2}<\theta<\frac{\pi}{2}\), add \(\pi\) to the result to get an angle in the desired interval
Step 4 ：Convert the result to radians and add \(2\pi\) to it until it falls within the desired interval \(\frac{3 \pi}{2}<\theta<2 \pi\)
Step 5 ：Final Answer: The solution to the equation \(\cot \theta=-\frac{1}{6}\) for \(\frac{3 \pi}{2}<\theta<2 \pi\) is \(\boxed{8.0191}\) radians
