4­1 Notes.notebook
November 04, 2013
4.1 Radian and Degree Measure
angles ­"trigonometry" is the measure of angles
angle ­ determined by rotating a ray (half­line) about its
endpoints
initial side ­ starting point of a ray
terminal side ­ position after rotation (ending point)
vertex ­ endpoint of ray
standard position ­ origin is vertex and initial side
coincides with x­axis EXAMPLE: 240
positive angles ­ generated by counterclockwise rotation
negative angles ­ clockwise rotation
coterminal ­ angles have same initial side and same
terminal side
Angles are labeled with Greek letters or capital letters
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4­1 Notes.notebook
November 04, 2013
80
90
100
110
70
60
110
50
100
90
30
150
130
140
50
130
140
70
60
120
40
120
80
0°
40
150
30
160
20
160
10
0
20
170
10
180
0
170
180
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4­1 Notes.notebook
November 04, 2013
Radian Measure ­ measure of angle determined by
amount of rotation from initial side to terminal side
central angle ­ vertex of angle at center of circle
Defn. of Radian ­ 1 radian is measure of a central angle that intercepts an arc S equal in length to the radius r of circle
~1 radian is approximately equal to 57 degrees
1/2 revolution = 1/4 revolution =
1/6 revolution =
Find coterminal angle by adding or subtracting 360
degrees.
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4­1 Notes.notebook
November 04, 2013
Ex. 1 Find the co­terminal angle.
a. θ = 13π/6
b. θ = -3π/4
Complementary angles ­ sum is 90 degrees
Supplementary angles ­ sum is 180 degrees
Ex. 2 a. complement of θ = 2π/5
supplement of θ = 2π/5
b. complement of θ = 4π/5
supplement of θ = 4π/5
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4­1 Notes.notebook
November 04, 2013
Degree measure ­ 2nd way to measure angle
To convert from:
degrees to radians multiply by π/180
radians to degrees multiply by 180/π
Ex. 3 Convert from degrees to radians
a. 30
c. 315
b. ­270
d. 83.7
Ex. 4 Convert from radians to degrees
a. 3π
c. 7π/3
b. ­π/2
d. -2
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4­1 Notes.notebook
November 04, 2013
ASSN: p. 265 3­17 odd, 23,27,31­47 odd, 53
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