Let us analyze the problem step by step.

Problem Explanation:

1. $\csc 270^\circ$:

   • $\csc \theta = \frac{1}{\sin \theta}$.
   • At $270^\circ$, $\sin 270^\circ = -1$.
   • Therefore, $\csc 270^\circ = \frac{1}{-1} = -1$.

2. $\cot 270^\circ$:

   • $\cot \theta = \frac{\cos \theta}{\sin \theta}$.
   • At $270^\circ$, $\cos 270^\circ = 0$ and $\sin 270^\circ = -1$.
   • Therefore, $\cot 270^\circ = \frac{\cos 270^\circ}{\sin 270^\circ} = \frac{0}{-1} = 0$.

Final Results:

• $\csc 270^\circ = -1$
• $\cot 270^\circ = 0$

Would you like further explanation or additional details?
Here are 5 follow-up questions for you to explore further:

1. What are the exact values for other trigonometric functions at $270^\circ$?
2. How do we calculate cosecant and cotangent for angles not on the unit circle?
3. Can we determine similar values for $90^\circ$, $180^\circ$, and $360^\circ$?
4. What does "undefined" mean for trigonometric functions?
5. Why is $\csc \theta$ undefined when $\sin \theta = 0$?

Tip: For trigonometric functions on the unit circle, always start by recalling $\sin$ and $\cos$ values for the given angle.