Question

What is the radian measure for an angle that measures 720 degrees?

Answer 1

4pi

Explanation:

on edg

Answer 2

720 degrees =
`(\pi)/(4)\ radians` or 0.785 radians.

Explanation:

Given:

The angle in degrees in given as 720°

We need to convert this to radians.

Now, we know that, the relation between degrees and radians is given as:

180 degree = π radians

Therefore, using unitary method, the value of 1 degree can be calculated.

∴ 1 degree =
`(\pi)/(180)\ radians`

Now, the value of 720 degrees can be calculated by multiplying the unit value and 720. So,

`720\ degrees=(\pi)/(180)* 720\ radians\\\\ 720\ degrees =(720\pi)/(180)\\\\720\ degrees =(\pi)/(4)\ radians=0.785\ radians`

Hence, the measure of 720 degrees in radians is
`(\pi)/(4)\ radians` or 0.25π radians or 0.785 radians.