Question

Which of the following radian measures is equal to 540 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 to radians, you can use the conversion factor \( \frac{\pi \text{ radians}}{180^\circ} \).

To convert 540 degrees to radians, use the following formula:

\[
\text{Radians} = \text{Degrees} \times \frac{\pi \text{ radians}}{180^\circ}
\]

Now fill in the value:

\[
\text{Radians} = 540^\circ \times \frac{\pi}{180^\circ}
\]

Now, simplify the calculation:

\[
\text{Radians} = 540 \times \frac{\pi}{180}
\]

\[
\text{Radians} = 3 \times \pi
\]

So, \( 540^\circ \) is equal to \( 3\pi \) radians.