Here is the graph of the polar function $r = \frac{1}{\sin \theta}$.

• As expected, there are vertical asymptotes at $\theta = 0, \pi, 2\pi$, where $\sin \theta = 0$, and the function becomes undefined.
• The graph is symmetric about the y-axis and exhibits large values as it approaches the asymptotes.

Would you like more details about this graph or its behavior?

Here are some related questions to explore further:

1. How does the graph of $r = \frac{1}{\cos \theta}$ compare to this one?
2. What happens if we modify the equation to $r = \frac{1}{\sin^2 \theta}$?
3. Can you explain the behavior of polar graphs for other trigonometric functions?
4. How does symmetry in polar graphs work for different functions?
5. What does the graph of $r = \frac{1}{\sin(\theta + \frac{\pi}{4})}$ look like?

Tip: When analyzing polar graphs, always check for points where the function might become undefined or infinite.