The given equation is in polar form:

$r \sin \theta = 3$

We want to convert it into rectangular coordinates. The conversion formulas from polar to rectangular coordinates are:

$x = r \cos \theta \quad \text{and} \quad y = r \sin \theta$

Since the equation contains $r \sin \theta$, we can directly substitute $y$ for $r \sin \theta$:

$y = 3$

Thus, the equation in rectangular coordinates is:

$y = 3$

This represents a horizontal line at $y = 3$ in the Cartesian plane.

Would you like me to graph this for you or provide more details?

Here are 5 follow-up questions you might explore:

1. What are the conversions for $r \cos \theta$ and $r^2$ in rectangular coordinates?
2. How would you convert the equation $r = 2 \sin \theta$ into rectangular coordinates?
3. Can a polar equation result in a vertical line in rectangular form?
4. What is the general process for converting a polar equation of the form $r = f(\theta)$ to rectangular coordinates?
5. How would you solve $r \cos \theta = 2$ in rectangular coordinates?

Tip:

When converting polar equations to rectangular coordinates, always look for recognizable components like $r \sin \theta$, $r \cos \theta$, or $r^2$ to simplify the process.