Question
Which of the following radian measures is equal to 360 degrees?
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi.)
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi.)
Answers
GPT-4o mini
The relationship between degrees and radians is given by the formula:
\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]
To convert 360 degrees to radians, we use the formula:
\[
\text{radians} = 360 \times \frac{\pi}{180}
\]
Calculating this, we have:
\[
\text{radians} = 360 \times \frac{\pi}{180} = 2\pi
\]
Therefore, the radian measure that is equal to 360 degrees is \(2\pi\).
\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]
To convert 360 degrees to radians, we use the formula:
\[
\text{radians} = 360 \times \frac{\pi}{180}
\]
Calculating this, we have:
\[
\text{radians} = 360 \times \frac{\pi}{180} = 2\pi
\]
Therefore, the radian measure that is equal to 360 degrees is \(2\pi\).