Question
Which of the following degree measures is equal to 3 pi 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
To convert from radians to degrees, you can use the conversion factor that \( \frac{180 \text{ degrees}}{\pi \text{ radians}} \).
Given \( 3\pi \) radians, the conversion to degrees can be calculated as follows:
\[
3\pi \text{ radians} \times \frac{180 \text{ degrees}}{\pi \text{ radians}} = 3 \times 180 \text{ degrees}
\]
Now perform the multiplication:
\[
3 \times 180 = 540 \text{ degrees}
\]
Therefore, \( 3\pi \) radians is equal to \( 540 \) degrees.
Given \( 3\pi \) radians, the conversion to degrees can be calculated as follows:
\[
3\pi \text{ radians} \times \frac{180 \text{ degrees}}{\pi \text{ radians}} = 3 \times 180 \text{ degrees}
\]
Now perform the multiplication:
\[
3 \times 180 = 540 \text{ degrees}
\]
Therefore, \( 3\pi \) radians is equal to \( 540 \) degrees.