Question

Convert the given radian measure to a degree measure. -1.7π

Answer 1

`-306^\circ`

Explanation:

The conversion from radians to degrees is

`2\pi~rad = 360^\circ`

Dividing both sides by 2, you get

`\pi~rad = 180^\circ`

Divide both sides of the conversion equation just above by pi radians.

`(\pi~rad)/(\pi~rad) = (180^\circ)/(\pi~rad)`

`1 = (180^\circ)/(\pi~rad)`

The fraction on the right side is the conversion factor from radians to degrees. Since it equals 1, when you multiply a radian measure by it, you don't change the amount since it equals 1. You just change the units.

`-1.7\pi ~rad * (180^\circ)/(\pi~rad) = -1.7 * 180^\circ = -306^\circ`