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### From Degrees to Radians

```
Date: 09/22/98 at 18:31:19
From: Little Fairy
Subject: Radians

Nine degrees equals how many radians?

How do you solve problems like this? What are radians?
```

```
Date: 09/22/98 at 18:45:28
From: Doctor Pat
Subject: Re: Radians

If you make an angle at the center of a circle and extend it out until
the two rays of the angle cut the circle, the angle can be measured in
two ways. The first would be the degree measure that you know of; the
second would be to use the length of the arc of circle between the two
rays of the angle.

Notice that if we do this, the measurement will be different for
different-size circles. This is not true for degree measure of angles.
To correct for the different sizes of circles, the arc length is
divided by the length of a radius of the circle, and this measurement
is called radians. An angle that has a measure of 1 radian would cut an
arc equal to the length of 1 radius of whatever size circle you drew
(try it).

Since we know it takes 2*pi radii to reach around a circle
(circumference = 2*pi*r), and that a circle has 360 degrees, we can
use this relation to convert between degrees and radians. To convert
9 degrees to radians we set up a proportion like this:

9       ?
----- = -----
360     2*pi

and solve. In this case 18*pi/360 is the answer, but you might want to
make that a decimal or reduce the fraction.

I hope this helps a little. You may find some more information at David
Joyce's "A short course in trigonometry." Look at number 4: Angle
measurement.

http://aleph0.clarku.edu/~djoyce/java/trig/

- Doctor Pat, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Conic Sections/Circles
Middle School Geometry
Middle School Terms/Units of Measurement

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