Question

Which is a greater angle of rotation? 720° or 6π radians? Explain how you know.

Answer 1

Answer: the angle would be much greater because the angle calculated up to over 12 radians

Explanation:

Answer 2

`\boxed {\boxed {\sf 6 \pi \ radians}}`

Explanation:

It's hard to compare degrees and radians, so we should convert, then compare.

To convert radians to degrees, we multiply by 180 over pi. This way, the pi will cancel out when dividing.

`radian * \frac {180}{\pi}`

`6 \pi * \frac {180}{\pi}`

`\frac {1080 \pi}{\pi} \\`

`1080`

6π radians is equal to 1080 degrees, which is much larger than 720 degrees, so it is the greater angle of rotation.