Question

Trigonometry

Arc Length and Radian Measure
Solve the following problem.
Convert 4π/6 radians to degrees.

Answer 1

`(4 \pi)/(6)` radians is equal to 120°.

Explanation:

Step 1:

If an angle is represented in radians, it will be of the form
`(\pi)/(x)` radians.

If an angle is represented in degrees, it will be of the form x°.

To convert radians to degrees, we multiply the radian measure by
`(180)/(\pi) .`

For the conversion of radians to degrees,

the radians in degrees = (given value in radians)(
`(180)/(\pi)`).

Step 2:

To convert
`(4 \pi)/(6)`,

`((4 \pi)/(6))((180)/(\pi) ) = (4)(30),`

`(4)(30) = 120.`

So
`(4 \pi)/(6)` radians is equal to 120°.