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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
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