Angles in Degree & Radian Measurew/Unit Circle

Angle MeasureStandard 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-axisTerminal side: the other side of the angle.

y

x

Angle Measure o

Unit circle ANGLE MEASURE

?

300

600

00

?

?

?

?

?

?

?

450

900

1350

1800

2250

2700

3150

3600

1200

1500

2100

24003000

3300

Degree measureHow many degrees in a circle? (One full

revolution)y

x 0o

90o

180o

270o

360o

The measure is negative when the rotation is clockwise.

0o & 3600 are Coterminal

angles b/c they have the same terminal side y

x

o225

What is a angle that is coterminal with -225o?

?135o

Is 495o coterminal with the above angles?

White board practice

y

x

45o ?

45o315o ?

315o

-150o ?

-150o

Sketch each angle, can you find another that is coterminal?

-315o405o

-45o 675o

210o -510o

-60o

Radian MeasuresRadian is a another unit of measure for angles (in

terms of pi)To convert Degree measure to Radians multiply byo180

y

x

-60o

Convert to radian measure

oo

18060

o

o

180

60

R3

3

150o15

0o o180150

180

150

R6

5

6

5

Convert to degree measure

2

o90

20

3 o27

o180To convert Radians measure to Degree multiply by

Unit circle ANGLE MEASURERADIANS

300

600

?

?

?

?

?

?

450

900

1350

1800

2250

2700

3150

1200

1500

2100

24003000

3300

2

6

4

3

2

3

2

4

3

6

5

6

7

4

5

3

4

2

33

5 4

7 6

11

360o

Draw an angle with the given measure.

Look at unit circle: can you

find it?

It might help to convert to degrees

Answer:

350o

Answer:

4

3

Practiceangle measure: pg 832 #13-25Radians pg 840 #7-15 odd, 26-33

HomeworkWorkbook pg 343 #4-11Work book pg 347 #1-11, 21-26