graph the polar function on the given interval. r

Here's the graph of the polar function $r = 2 + \sin(\theta)$ over the interval $[0, 2\pi]$. The plot shows how the radius $r$ changes with respect to the angle $\theta$ in polar coordinates.

Would you like a detailed explanation of the graph or further assistance?

Here are five related questions to explore:

1. How would the graph change if the function was $r = 2 - \sin(\theta)$?
2. What happens if we add a constant multiplier to $\sin(\theta)$, such as $r = 2 + 2\sin(\theta)$?
3. How do you find the points of symmetry in polar graphs?
4. What is the area enclosed by the polar curve $r = 2 + \sin(\theta)$?
5. How do you convert this polar equation into Cartesian coordinates?

Tip: When analyzing polar graphs, always consider how the radius $r$ behaves at specific angles like $0$, $\frac{\pi}{2}$, $\pi$, and $\frac{3\pi}{2}$.