1. Angles in Degree & Radian Measure w/Unit Circle
Unit 6 Trig
Angles in Degree & Radian Measure
w/Unit Circle

2. Angle Measure
Standard Position: an angle in the coordinate plane with vertex at the origin and one ray(side) on the positive x-axis.
Initial side: the ray on the x-axis
Terminal side: the other side of the angle. y x
Angle Measure o

3. Unit circle 900 ? 1200 600 ANGLE MEASURE ? 450 ? 1350 300 1500 3600
1800 00 ? ?
2100
3300
2250 ?
3150 ?
2400
3000
2700 ?

4. 0o & 3600 are Coterminal angles b/c they have the same terminal side
Degree measure
What is a angle that is coterminal with -225o?
0o & 3600 are Coterminal angles b/c they have the same terminal side
How many degrees in a circle? (One full revolution)
90o y x y x
135o ?
180o
360o
270o 0o
Is 495o coterminal with the above angles?
The measure is negative when the rotation is clockwise.

5. White board practice 315o ? 45o ? -150o ? -315o 405o 210o -510o -45o
Sketch each angle, can you find another that is coterminal?
-315o
405o
315o ?
45o ?
-150o ?
45o y x
-150o
315o
210o
-510o
-45o
675o

6. Radian Measures
Radian is a another unit of measure for angles (in terms of pi)
To convert Degree measure to Radians multiply by
To convert Radians measure to Degree multiply by
Convert to radian measure
Convert to degree measure y x
150o
-60o
150o
-60o

7. Unit circle 900 ? 1200 600 ANGLE MEASURE RADIANS 450 ? 1350 300 1500
1800
360o ?
2100
3300
2250 ?
3150 ?
2400
3000
2700 ?

8. Draw an angle with the given measure.
It might help to convert to degrees
Look at unit circle: can you find it?

9. Answer:
350o

10. Answer:

12. Practice
angle measure: pg 832 #13-25
Radians pg 840 #7-15 odd, 26-33

13. Homework
Workbook pg 343 #4-11
Work book pg 347 #1-11, 21-26