Chapter 3
Section 3.1
Chapter 3: Radian Measure and the Unit Circle
Section 3.1: Radian Measure
I.
Radian Measure

Technical Definition: An angle with its vertex at the center of a circle that intercepts an arc on
the circle equal in length to the radius of the circle has a measure of 1 radian.

Practical Definition: There are 2 radians in a full circle, and thus is the same as 360°.
II.
Converting Between Degrees and Radians
Converting Between Degrees and
Radians

Multiply a degree measure by

Multiply a radian measure by

and simplify to convert to radians.
180
180

and simplify to convert to degrees.
Example 1 (Converting Degrees to Radians): Convert each degree measure to radians.
a) 108˚
b) -135˚
c) 325.7˚
Chapter 3
Section 3.1
Example 2 (Converting Radians to Degrees): Convert each radian measure to degrees.
a)
11
12
b) 
7
6
c)
Practice: How many degrees are there in 1 radian?
Agreement on Angle
Measurement Units

Radians is not a unit of measurement like degrees, feet, or centimeters.

If no unit of angle measure is specified, then the angle is understood to be
measured in radians.
Chapter 3
Section 3.1
Here are the eight most important equivalences between degrees and radians. You should know
these as quickly as possible!
Chapter 3
III.
Section 3.1
Finding Function Values of Angles in Radian Measure

The values of our six favorite trigonometric functions can now be found for angles measured in
radians by first converting to degree measure.

Advice: Become comfortable with radian measure as soon as possible, so that you can
evaluate functions without needing to convert.
Example 3(Finding Function Values of Angles in Radian Measure): Find each value.
 5 
a) cos 

 6 
 3 
b) cot  
 4 
 5 
c) sec  
 3 