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The problem is asking to convert the polar coordinate \((-8, -222^\circ)\) to rectangular coordinates.

### Solution:

1. **Identify the polar coordinates:** 
   - \( r = -8 \)
   - \( \theta = -222^\circ \)

2. **Convert \( \theta \) to a positive equivalent angle (optional):**
   - Since angles can be represented by adding multiples of \(360^\circ\), we have:
     \[
     -222^\circ + 360^\circ = 138^\circ
     \]
   - So, \( \theta = -222^\circ \) is equivalent to \(138^\circ\).

3. **Use the polar-to-rectangular conversion formulas:**
   - \( x = r \cos \theta \)
   - \( y = r \sin \theta \)

4. **Calculate \( x \) and \( y \):**
   \[
   x = -8 \cos(138^\circ)
   \]
   \[
   y = -8 \sin(138^\circ)
   \]

5. **Compute the values of \( \cos(138^\circ) \) and \( \sin(138^\circ) \):**
   - \( \cos(138^\circ) \approx -0.7431 \)
   - \( \sin(138^\circ) \approx 0.6691 \)

6. **Substitute these values:**
   \[
   x \approx -8 \times -0.7431 = 5.9448
   \]
   \[
   y \approx -8 \times 0.6691 = -5.3528
   \]

7. **Final answer:**
   \[
   (x, y) \approx (5.9448, -5.3528)
   \]

So, the rectangular coordinates are approximately \((5.94, -5.35)\).

Would you like further details or have any questions?

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### Related Questions:

1. How do you handle negative values for \( r \) in polar coordinates?
2. What is the general formula for converting polar coordinates to rectangular coordinates?
3. How can we convert rectangular coordinates back to polar coordinates?
4. What is the significance of using positive vs. negative angles in polar coordinates?
5. How would this conversion change if the angle were measured in radians?

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### Tip:
When dealing with polar coordinates, remember that a negative radius flips the direction by \(180^\circ\), which can sometimes simplify conversions.

Convert -8∠-222° to rectangular coordinates.

Convert the polar coordinate (-8, -222°) to rectangular coordinates using polar-to-rectangular conversion formulas. The solution covers key trigonometric concepts and provides a step-by-step approach to find the rectangular coordinates for the given angle.

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