Math Problem Statement

Convert 9π/5 to degrees.

Solution

To convert 9π5\frac{9\pi}{5} radians into degrees, we use the conversion formula:

Degrees=Radians×180π\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}

So, applying this to 9π5\frac{9\pi}{5}:

9π5×180π=9×1805=16205=324\frac{9\pi}{5} \times \frac{180^\circ}{\pi} = \frac{9 \times 180^\circ}{5} = \frac{1620^\circ}{5} = 324^\circ

Thus, 9π5\frac{9\pi}{5} radians is equal to 324 degrees.

Would you like further clarification or details?

Here are five related questions to explore:

  1. How do you convert degrees back into radians?
  2. What is the significance of π\pi in radian measures?
  3. What is the general process for converting angles between radians and degrees?
  4. Can you describe why 180180^\circ corresponds to π\pi radians?
  5. What is the difference between a positive and negative angle in this context?

Tip: Always remember that π\pi radians corresponds to 180180^\circ, making it easier to switch between radians and degrees.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Angle Conversion
Radians to Degrees

Formulas

Degrees = Radians × (180° / π)

Theorems

Radian-Degree Conversion Theorem

Suitable Grade Level

Grades 9-12