Transcript Holt Geometry 3-1

3-1 Lines and Angles
Paper for notes
Pearson 13.3
Holt Geometry
TOPIC:
Name: Daisy Basset
Date :
Period:
3-1 Lines and Angles
13.3
Radian
Measure
Objective:
Notes
Understand radian
measure of an angle as
the length of the arc on
the unit circle included
by the angle.
Holt Geometry
Key Concept
3-1 Lines and Angles
 Proportion Relating
Radians & Degrees
 Converting Between
Radians & Degrees
 Length of an
Intercepted Arc
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3-1 Lines and Angles
Vocabulary
 Central Angle
 Intercepted
Arc
 Radian
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3-1 Lines and Angles
Notes 13.3
13.3 Handout
Calculator
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1. Find the
measure in
degrees or
in radians.
3-1 Lines and Angles
Holt Geometry
A. What is the
degree of
measure of an
 3
angle of
4
radians?
3-1 Lines and Angles
Holt Geometry
and Angles
3-1 Lines
radians 
degrees
180
Multiply by
 radians
180
 3 radians


 radians
4
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3-1 Lines and Angles
 3  180

4
135
 3
An angle of
radians
4
measures _____.
135
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B. What is the
radian
measure of
an angle of
27º?
3-1 Lines and Angles
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and Angles
3-1 Lines
degrees 
Multiply by
radians
 radians
180
3
27  radians


1
180
20
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An angle of
3-1 Lines and Angles
27º measures
3
__ radians.
20
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C. What is the
degree of
measure of an

angle of
2
radians?
3-1 Lines and Angles
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and Angles
3-1 Lines
radians 
degrees
180
Multiply by
 radians
 radians
2
1
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90
180


 radians

An angle of
2
radians
3-1 Lines and Angles
measures ___.
90
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2. Find the
exact values
and then
round to the
th
nearest 100 .
3-1 Lines and Angles
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3-1 Lines and Angles

4
A. cos ( radians)
sin ( radians)

4
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3-1 Lines and Angles

4
cos ( radians) =
2
2
≈
sin

(4
radians) =
≈
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0.71
2
2
0.71
3-1 Lines and Angles7
B. cos (
6
radians)
sin (
7
6
radians)
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3-1 Lines and Angles
cos
7
(6
radians)
 3
= 2
≈  0.87
sin (
7
6
radians) =
1
2
≈  0.50
Holt Geometry
3. Use the given
circle and find
the arc length.
Round to the
th
nearest 10 .
3-1 Lines and Angles
Holt Geometry
A. Find s.
3-1 Lines and Angles
arc length = radius•m central 
s=
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5
3• 6
3-1 Lines and Angles
1
s=
3 5

1 6
2
s=
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5
in. 
2
7.9 in
Summary
3-1 Lines and Angles
Explain how to
convert degrees to
radians and radians
to degrees.
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3-1 Lines and Angles
Hmwk 13.3 A:
Practice: 7 – 33 ODDS
Work on the Study Plan
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Practice:
Lines13.3
andA:Angles
3-1 Hmwk
Holt Geometry
7 – 33 ODDS ONLY
3-1 Lines and Angles
Notes 13.3
13.3 Handout
Calculator
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B. Find b.
3-1 Lines and Angles
arc length = radius•m central 
b
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2
= 3• 3
3-1 Lines and Angles
1
b=
3 2

1 31
b = 2 in.  6.3 in.
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4. The length of a
windshield wiper
arm is 20 in. and
it rotates
through an angle
of 105º.
3-1 Lines and Angles
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3-1 Lines and Angles
What is the length of
the arc to the
nearest inch that the
wiper arm travels as
it moves across the
windshield.
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3-1 Lines and Angles
x
105º
20 in
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3-1 Lines and Angles
arc length = radius•m central 
(in radians)
degrees  radians
Multiply by
 radians
180
105  radians


180
1
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3-1 Lines and Angles
arc length = radius•m central 
(in radians)
x
105

36
.
6519
= 20• 180
The wiper arm travels
37 in. as it moves
about _____
across the windshield.
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Summary
3-1 Lines and Angles
Explain how to find
an arc length given
a radius and
measure of the
central angle.
Holt Geometry
Hmwk 13.3 B:
Math XL
3-1 Lines and Angles
Work on the Study Plan
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