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Measuring
MeasuringAngles
AnglesininRadians
Radians
12-3-EXT
12-3-EXT
Lesson Presentation
HoltMcDougal
GeometryGeometry
Holt
12-3-EXT
Measuring Angles in Radians
Objectives
Use proportions to convert angle measures
from degrees to radians.
Holt McDougal Geometry
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Measuring Angles in Radians
Vocabulary
radian
Holt McDougal Geometry
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Measuring Angles in Radians
One unit of measurement for angles is
degrees, which are based on a fraction
of a circle. Another unit is called a radian,
which is based on the relationship of the
radius and arc length of a central angle
in a circle.
Holt McDougal Geometry
12-3-EXT
Measuring Angles in Radians
If a central angle θ in a circle of radius r intercepts an arc
of length r, the measure of θ is defined as 1 radian. Since
the circumference of a circle of radius r is 2πr, an angle
representing one complete rotation measures 2π
radians, or 360°.
2π radians = 360° and π radians = 180°
π radians
1° =
180°
180°
and 1 radian = π radians
Use these facts to convert between radians and degrees.
Holt McDougal Geometry
12-3-EXT
Measuring Angles in Radians
Holt McDougal Geometry
12-3-EXT
Measuring Angles in Radians
Example 1: Converting Degrees to Radians
Convert each measure from degrees to radians.
A. 85°
17
85°
π radians
180° 36
= 17 π
36
π radians
180° 2
=
A. 90°
1
90°
Holt McDougal Geometry
π
2
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Measuring Angles in Radians
Example 2: Converting Radians to Degrees
Convert each measure from radians to degrees.
A.
1
2π
3
2 π radians
3
60
Π
180°
radians
= 120°
180°
radians
= 30°
π
6
B.
1
π radians
6
Holt McDougal Geometry
30
Π