Math Problem Statement

how many degrees in a pi radians

Solution

There are 180 degrees in π\pi radians.

This is because the relationship between degrees and radians is:

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

Substituting π\pi for radians:

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

Would you like further clarification or examples? Here are some related questions to explore:

  1. How many radians are in 360 degrees?
  2. What is the degree measure of π2\frac{\pi}{2} radians?
  3. How can you convert 45 degrees to radians?
  4. What is the general formula to convert between radians and degrees?
  5. Why is π\pi radians equal to 180 degrees?

Tip: Always remember to include π\pi in your calculations when working with radians; it's the key constant in these conversions.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Radians and Degrees Conversion

Formulas

Degrees = Radians × (180/π)

Theorems

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Suitable Grade Level

Grades 8-10