1. Radian and Degree Measure
MAT 200
Radian and Degree Measure
In this section, we will study the following topics:
Terminology used to describe angles
Degree measure of an angle
Radian measure of an angle
Converting between radian and degree measure

2. Angles
Trigonometry: measurement of triangles
Angle Measure

3. Standard Position Vertex at origin
The initial side of an angle in standard position is always located on the positive x-axis.

4. Positive and negative angles
When sketching angles, always use an arrow to show direction.

5. Measuring Angles
The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.
There are two common ways to measure angles, in degrees and in radians.
We’ll start with degrees, denoted by the symbol º.
One degree (1º) is equivalent to a rotation of of one revolution.

6. Measuring Angles

7. Ex1: Name the quadrant in which each angle lies. 50º 208º II I
Classifying Angles
Angles are often classified according to the quadrant in which their terminal sides lie.
Ex1: Name the quadrant in which each angle lies.
50º
208º II I
-75º III IV
Quadrant 1
Quadrant 3
Quadrant 4

8. Classifying Angles
Standard position angles that have their terminal side on one of the axes are called quadrantal angles.
For example, 0º, 90º, 180º, 270º, 360º, -90º, -180º, º, -360º … are quadrantal angles.

9. A second way to measure angles is in radians.
Radian Measure
A second way to measure angles is in radians.
Definition of Radian:
One radian is the measure of a central angle  that intercepts arc s equal in length to the radius r of the circle.
In general,

10. Find the radian measure of an angle with radius 5 in
Find the radian measure of an angle with radius 5 in. and arc length 9 in.

11. Radian Measure

12. Radian Measure

13. Conversions Between Degrees and Radians
To convert degrees to radians, multiply degrees by
To convert radians to degrees, multiply radians by

14. Ex 5. Convert the degrees to radian measure.
60
30
-54
-118
45

15. Ex 6. Convert the radians to degrees.
a) b) c) d)

16. Degree and Radian Form of “Special” Angles
0° 
360 ° 
30 ° 
45 ° 
60 ° 
330 ° 
315 ° 
300 ° 
 120 °
 135 °
 150 °
 240 °
 225 °
 210 °
 180 °
90 ° 
270 °  
Degree and Radian Form of “Special” Angles

17. Ticket out the Door! Convert from degrees to radians. 54 -300
Convert from radians to degrees. 3. 4.