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

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 \((0, 0)\).