1. 6.1 Radian and Degree Measure
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.

2. 6.1 Radian and Degree Measure
Measuring Angles

3. 6.1 Radian and Degree Measure
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,

4. 6.1 Radian and Degree Measure
Radian Measure

5. 6.1 Radian and Degree Measure
Radian Measure

6. 6.1 Radian and Degree Measure
Conversions Between Degrees and Radians
To convert degrees to radians, multiply degrees by
To convert radians to degrees, multiply radians by

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

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

9. Ex 7. Find one positive and one negative angle that is coterminal with the angle  = in standard position.
Ex 8. Find one positive and one negative angle that is coterminal with the angle  = in standard position.

10. 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

11. Class Work Convert from degrees to radians. 54 -300
Convert from radians to degrees. 3. 4.

12. Find one postive angle and one negative angle in standard position that are coterminal with the given angle.
135

13. HW p odd, 37-41odd, 43-47odd