The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math


Date: 9/2/96 at 22:52:58
From: Mohd Nasir Mahmud
Subject: Radians

Dear Sir,

Could you tell me why pi radians = 180 degrees?

Date: 10/24/96 at 16:5:50
From: Doctor Jaime
Subject: Radians

This is an immediate consequence of the definition of radians and 
degrees.  In fact 1 radian is defined as the central angle subtended 
by the arc of length 1 on a unit circle.  1 degree is the central 
angle subtended by (1/360)th of the circumference of a unit  circle. 

This measure dates back to the Babylonians, who used a base 60 
number system. Since the circumference of the unit circle is 2 Pi, 
it follows that there are 2 Pi radians in 360 degrees, or 
Pi radians = 180 degrees.

-Doctor Jaime,  The Math Forum
Check out our web site!   
Associated Topics:
Middle School Pi
Middle School Terms/Units of Measurement

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.