Question

Which of the following radian measures is equal to 2,880 degrees?
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi)

Answer 1

To convert degrees into radians, we can use the conversion factor where \( \pi \) radians is equivalent to \( 180 \) degrees.

Given that we want to convert \( 2880 \) degrees to radians, we can use the formula:

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

Substituting \( 2880 \) degrees into this formula, we have:

\[
\text{radians} = 2880 \times \frac{\pi}{180}
\]

Now we can simplify this:

\[
\text{radians} = 2880 \div 180 \times \pi
\]

Calculating \( 2880 \div 180 \):

\[
2880 \div 180 = 16
\]

Thus,

\[
\text{radians} = 16\pi
\]

Therefore, the radian measure that is equal to \( 2880 \) degrees is:

\[
\boxed{16\pi}
\]