Radians and Degrees

Date: Mon, 21 Nov 1994 15:31:39 -0900
From: Patryce McKinney

Why are radians preferable to degree measures?

Patryce 
wvhppdm@northstar.k12.ak.us
Fairbanks, Alaska

Date: Mon, 21 Nov 1994 20:00:54 +0000
From: Elizabeth Weber

Hi Patryce!  

     The only reason I know of that radians are often preferable to
degree measures is that when you're expressing things in radians, they 
LOOK more like fractions of a circle.  If you see a number like 3p/2 
radians, it looks a lot more like 3/4 of a circle (which it is) than a 
number like 270 degrees, even though 270 degrees means exactly the 
same thing.

     Perhaps some of the other math doctors know other reasons--if they 
do, you'll hear from them too!
                            Thanks for writing to Dr. Math,
                                        Elizabeth, a math doctor

Date: 30 Nov 1994 16:38:34 GMT
From: Math Doctor
Organization: Swarthmore College

Hello there Patryce!

     Here's the main reason I know of that people like radians better than
degrees.  Do you know how to find out the arc length of part of a circle? 
You take the fraction (like 1/3, or 3/7 or something) of the circle that
that arc is, and you multiply that by the total circumference of the
circle.  Well, as it turns out, when you use degrees, you have to have
some nasty conversion factor in there to figure out the fraction of the
circle that the arc is, but when you use radians, you just multiply (the
angle subtended by the arc, measured in radians) times (the radius of the
circle).  A nice formula.  Try to derive the formula for the length of an
arc of a circle, given the degree measure of the angle that subtends it. 
Is it a nice formula?

     The way things work out, the formula for arc length is used to derive 
a whole bunch of other things.  So it makes sense to use the units that 
will make everything come out nicely.

     If you have any more questions, be sure to write back!

-Ken "Dr." Math