Math 1316
Section 3.1 Class Notes
Radian Measure
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.
Converting Between Degrees and Radians

radian and simplify to convert to radians.
180
180
2. Multiply a radian measure by
and simplify to convert to degrees.

1. Multiply a degree measure by
Example 1: Convert each degree measure to radians.
1. 450
2. -2700
1
Math 1316
Section 3.1 Class Notes
3. 249.80
Example 2: Convert each radian measure to degrees.
1.
9
4
2. 
5
6
3. 4.25
Agreement on Angle Measurement Units
If no unit of angle measure specified, then the angle is understood to be measured in radian.
2
Math 1316
Section 3.1 Class Notes
Special Acute Angles
0o
0
30o
π/6
45o
π/4
sin θ
cos θ
tan θ
Special Angles on Circle
3
60o
π/3
90o
π/2
Math 1316
Section 3.1 Class Notes
Finding Function Values for Angles in Radians
Example 1: First convert the radian measure into degree then find the exact value of the given
expression without using a calculator.
1. cos
2. cot
3. tan

6

3
5
6
4
Math 1316
Section 3.1 Class Notes
 
4. cos  
 6
 11 
5. csc 

 3 
5