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.

Learn how to graph the polar function r = 1/sin(θ) and understand the behavior of the function near vertical asymptotes at θ = 0, π, 2π. This problem involves key trigonometric concepts and introduces polar coordinate graphing, ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation