Section 4.1
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Trigonometry: the measurement of angles
Standard Position: Angles whose initial side
is on the positive x-axis
90º
terminal
0º
180º
initial
vertex
270º
1.) 50º
2.) 130º
3.) 260º
4.) 310º
1.) -50º
2.) -180º
3.) -240º
4.) -300º
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Angles that share the same terminal side
Differ by 360º (or a multiple of 360 ie. 720)
Example 4 vs example 1
To find positive and negative coterminal
angles- add and subtract 360º
1.) 210º
2.)-180º
3.) 400º
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Radians are a 2nd way to measure an angle
Positive and negative radian measures:
1.) 5
6

3.) 4
2.) 6
5
4.) 11
6
1.)
5
6
2.)
3
7
3.)
9
5
4.)
13
4
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Differ by 2
To find a positive and negative coterminal
angle, add and subtract 2
1.) 3
2.)
3
4
5
3.)
6

Degree to radian: Multiply by 180
1.)
2.)
3.)
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180
Radian to degree: Multiply by 
1.)
2.)
3.)
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Complementary angles- angles whose sum = 90
Supplementary angles- angles whose sum = 180
1.) 45º
2.) 61º
3.) 100º
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A degree, represented by the symbol °, is a
unit of angular measure equal to 1/180th of a
straight angle. In the DMS (degree-minutesecond) system of angular measure, each
degree is subdivided into 60 minutes
(denoted by ‘) and each minute is subdivided
into 60 seconds (denoted by “).
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Convert 37.425° to DMS.
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Convert 42°24’36” to degree.
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Arc length- measures a segment (arc) of a
circle
S

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S  r

must be in radians
1.) r  5,  3
4
2.) r  3,  4
5
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Degree Measure
Find the length of an
arc that subtends a
central angle with
measure 120 degrees in
a circle with a radius of
5 inches.
s
 r
180
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Angular speed is measured in units like
revolutions per minute.
Linear speed is measured in units like miles
per hour.
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Jaxen’s truck has wheels 36 inches in
diameter. If the wheels are rotating at 630
rpm (revolutions per minute), find the trucks
speed in miles per hour.
Page 265-268
11-19 odd, 40-46 even, 59-69 odd, 81-84 all, 96,
99
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