Question

How many radians are in a three-quarter rotation around a circle, or 270°?

(1 point)
Responses

pi radians
Image with alt text: pi radians

Start Fraction 3 pi over 2 End Fraction radians
Image with alt text: Start Fraction 3 pi over 2 End Fraction radians

2 pi radians
Image with alt text: 2 pi radians

3 pi radians

Answer 1

A three-quarter rotation around a circle is equivalent to 270 degrees. To convert degrees to radians, you can use the conversion factor where \( \pi \) radians is equal to 180 degrees.

To convert 270 degrees to radians, you can use the formula:

\[
\text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}}
\]

Applying that to 270 degrees:

\[
\text{radians} = 270 \times \frac{\pi}{180} = \frac{270\pi}{180} = \frac{3\pi}{2}
\]

So, a three-quarter rotation around a circle or 270° is equal to \( \frac{3\pi}{2} \) radians.

The correct answer is: **Start Fraction 3 pi over 2 End Fraction radians**.