Math Problem Statement

Fill in the table by selecting the correct answers for each conversion between degrees and radians.

Solution

This table involves converting between degrees and radians. I'll walk through the conversions:

  1. From Degrees to Radians:

    • Formula: radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}
  2. From Radians to Degrees:

    • Formula: degrees=radians×180π\text{degrees} = \text{radians} \times \frac{180}{\pi}

Let me help you with each of these conversions.


Let's go through each question step-by-step:

  1. Degrees to Radians (90°)
    Using the formula:
    radians=90×π180=π2\text{radians} = 90 \times \frac{\pi}{180} = \frac{\pi}{2}

  2. Degrees to Radians (45°)
    radians=45×π180=π4\text{radians} = 45 \times \frac{\pi}{180} = \frac{\pi}{4}

  3. Degrees to Radians (30°)
    radians=30×π180=π6\text{radians} = 30 \times \frac{\pi}{180} = \frac{\pi}{6}

  4. Radians to Degrees (π\pi)
    degrees=π×180π=180°\text{degrees} = \pi \times \frac{180}{\pi} = 180°

  5. Radians to Degrees (π3\frac{\pi}{3})
    degrees=π3×180π=60°\text{degrees} = \frac{\pi}{3} \times \frac{180}{\pi} = 60°

  6. Radians to Degrees (π5\frac{\pi}{5})
    degrees=π5×180π=36°\text{degrees} = \frac{\pi}{5} \times \frac{180}{\pi} = 36°

  7. Degrees to Radians (18°)
    radians=18×π180=π10\text{radians} = 18 \times \frac{\pi}{180} = \frac{\pi}{10}

  8. Degrees to Radians (12°)
    radians=12×π180=π15\text{radians} = 12 \times \frac{\pi}{180} = \frac{\pi}{15}

  9. Radians to Degrees (π9\frac{\pi}{9})
    degrees=π9×180π=20°\text{degrees} = \frac{\pi}{9} \times \frac{180}{\pi} = 20°

  10. Radians to Degrees (π12\frac{\pi}{12})
    degrees=π12×180π=15°\text{degrees} = \frac{\pi}{12} \times \frac{180}{\pi} = 15°

  11. Degrees to Radians (9°)
    radians=9×π180=π20\text{radians} = 9 \times \frac{\pi}{180} = \frac{\pi}{20}

  12. Radians to Degrees (π18\frac{\pi}{18})
    degrees=π18×180π=10°\text{degrees} = \frac{\pi}{18} \times \frac{180}{\pi} = 10°


Would you like further explanations on any of these steps?

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Math Problem Analysis

Mathematical Concepts

Radians and Degrees Conversion
Trigonometry
Basic Arithmetic

Formulas

Radians = Degrees × (π / 180)
Degrees = Radians × (180 / π)

Theorems

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Suitable Grade Level

Grades 8-10