To convert the polar equation $$ r=4 $$ to ectangular form, we use the relationship oetween polar and rectangular coordinates:

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To convert the polar equation $$ r = 4 $$ to its rectangular (Cartesian) form, we use the relationships between polar and rectangular coordinates:

$$
\begin{align*}
x &= r \cos \theta, \
y &= r \sin \theta, \
r^2 &= x^2 + y^2.
\end{align*}
$$

Here's the step-by-step conversion:

1. **Start with the given polar equation:**
   $$
   r = 4.
   $$

2. **Square both sides to utilize the relationship $$ r^2 = x^2 + y^2 $$:**
   $$
   r^2 = 16.
   $$

3. **Substitute $$ r^2 $$ with $$ x^2 + y^2 $$:**
   $$
   x^2 + y^2 = 16.
   $$

**Final Rectangular Form:**
$$
x^2 + y^2 = 16.
$$

**Interpretation:**
This equation represents a circle in the Cartesian coordinate system with a radius of 4 units centered at the origin $$(0, 0)$$.
The polar equation $$ r = 4 $$ converts to the rectangular form $$ x^2 + y^2 = 16 $$, which represents a circle with a radius of 4 units centered at the origin.

To convert the polar equation to
ectangular form, we use the relationship
oetween polar and rectangular
coordinates:

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To convert the polar equation to ectangular form, we use the relationship oetween polar and rectangular coordinates: