4.1. Angles in Radians and Degrees http://www.ck12.org
4.1 Angles in Radians and Degrees
Here you will learn how to translate between different ways of measuring angles.
Most people are familiar with measuring angles in degrees. It is easy to picture angles like 30◦, 45◦or 90◦and the
fact that 360◦makes up an entire circle. Over 2000 years ago the Babylonians used a base 60 number system and
divided up a circle into 360 equal parts. This became the standard and it is how most people think of angles today.
However, there are many units with which to measure angles. For example, the gradian was invented along with the
metric system and it divides a circle into 400 equal parts. The sizes of these different units are very arbitrary.
A radian is a unit of measuring angles that is based on the properties of circles. This makes it more meaningful than
gradians or degrees. How many radians make up a circle?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/58059http://www.youtube.com/watch?v=nAJqXtzwpXQ James Sousa: Radian Measure
Guidance
A radian is defined to be the central angle where the subtended arc length is the same length as the radius.
Another way to think about radians is through the circumference of a circle. The circumference of a circle with
radiusris 2πr. Just over six radii (exactly 2πradii) would stretch around any circle.
To define a radian in terms of degrees, equate a circle measured in degrees to a circle measured in radians.