Question

Change to radian measure

Answer 1

5a.
`(2 \pi)/(3)~rad`

5b.
`(7 \pi)/(6)~rad`

5c.
`(5 \pi)/(3)~rad`

Explanation:

The angle of a full circle is 2π radians.

The angle of a full circle is 360°.

That gives us enough information to create a formula to convert from degrees to radians and from radians to degrees.

2π radians = 360°

Divide both sides by 2.

π radians = 180°

Divide both sides by 180°.

(π rad)/(180°) = 180°/180°

(π rad)/(180°) = 1

Notice that the fraction (π rad)/(180°) = 1, and when you multiply a number by 1 you get the original number.

Now you can multuoply any degree measure by this fraction. the degrees cancel out,a nd you get radians. Also since the fraction equals 1, you are not changing the amount of degree. you are jus changi ng degrees to radians.

5a.

`120^\circ * (\pi ~rad)/(180^\circ) = (2 \pi)/(3)~rad`

5b.

`210^\circ * (\pi ~rad)/(180^\circ) = (7 \pi)/(6)~rad`

5c.

`300^\circ * (\pi ~rad)/(180^\circ) = (5 \pi)/(3)~rad`