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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.

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r sin θ = 3.

Learn how to convert the polar equation r sin θ = 3 into rectangular coordinates using the formula y = r sin θ, which simplifies to y = 3. This problem introduces core concepts of coordinate transformation, suitable for high school students in Grades 10-12.

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