Transcript Radian and Degree Measure

Compare the ratios sin A
and cos B
Compare the ratios sec A and csc B
Compare the ratios tan A and cot B
Warm up for 8.5
pg 618
Angle of Depression
Pg 622
At an altitude of 1,000 ft., a balloonist measures the angle
of depression from the balloon to the landing zone. The
measure of the angle is 15 degrees. How far is the balloon
from the landing zone?
Lots of room for notes on 623
Radian and Degree Measure
In this section, we will study the following
topics:
 Terminology used to describe angles
 Degree measure of an angle
 Radian measure of an angle
 Converting between radian and degree
measure
 Find coterminal angles
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Radian and Degree Measure
Angles
Trigonometry: measurement of triangles
Section 4.1, Figure 4.1, Terminal and
Angle Measure
Initial Side of an Angle , pg. 248
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Digital Figures, 4–2
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Radian and Degree Measure
Standard Position
Section 4.1, Figure 4.2, Standard
Position of an Angle, pg. 248
Vertex at origin
Copyright © Houghton Mifflin Company. All rights reserved.
The initial side of an angle
in standard position is always located
on the positive x-axis.
Digital Figures, 4–3
5
Radian and Degree Measure
Positive and Section
negative4.1,
angles
Figure 4.3, Positive and
Negative Angles, pg. 248
When sketching angles,
always use an arrow to
show direction.
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Digital Figures, 4–4
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Radian and Degree Measure
Measuring Angles
The measure of an angle is determined by the amount of
rotation from the initial side to the terminal side.
There are two common ways to measure angles, in degrees
and in radians.
We’ll start with degrees, denoted by the symbol º.
1
One degree (1º) is equivalent to a rotation of
360
revolution.
of one
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Radian and Degree Measure
Section 4.1, Figure 4.13, Common Degree
Measures on the Unit Circle, pg. 251
Measuring Angles
1
360
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Digital Figures, 4–9
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Radian and Degree Measure
Classifying Angles
Angles are often classified according to the quadrant
in which their terminal sides lie.
Ex1: Name the quadrant in which each angle lies.
50º
Quadrant 1
208º
Quadrant 3
II
I
-75º
Quadrant 4
III
IV
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Radian and Degree Measure
Classifying Angles
Standard position angles that have their terminal side
on one of the axes are called quadrantal angles.
For example, 0º, 90º, 180º, 270º, 360º, … are
quadrantal angles.
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Radian and Degree Measure
Radian Measure
A second way to measure angles is in radians.
Definition of Radian:
4.1, Figure
Illustration
One radian isSection
the measure
of a 4.5,
central
angle ofthat intercepts
pg. r249
arc s equal in lengthArc
to Length,
the radius
of the circle.
In general,
s

r
11
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Digital Figures, 4–6
Radian and Degree Measure
Radian Measure
2  6.28
  3.14
2 radians corresponds to 360
 radians corresponds to 180

2
radians corresponds
904.6, Illustration of
Section 4.1,to
Figure
Six Radian Lengths, pg. 249
Copyright © Houghton Mifflin Company. All rights reserved.

2
Digital Figures, 4–7
 1.57
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Radian and Degree Measure
Common
Section 4.1, Figure 4.7,
Radian Measure
Radian Angles, pg. 249
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Radian and Degree Measure
Conversions Between Degrees and Radians
1.
2.
To convert degrees to radians, multiply degrees by
To convert radians to degrees, multiply radians by

180
180

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Ex 5. Convert the degrees to radian
measure.
a)
60
b)
30
c)
-54
d)
-118
e)
45
Ex 6. Convert the radians to degrees.

a)
6

b)
2
11
c) 
18

d)
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Degree and Radian Form of “Special” Angles
90 ° 
 120 °
60 ° 
 135 °
45 ° 
 150 °
30 ° 

0° 
 180 °
360 ° 
 210 °
330 ° 
 225 °
315 ° 
 240 °
300 ° 
270 ° 
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Class Work
Convert from degrees to radians.
1. 54
2. -300
Convert from radians to degrees.
3. 11
3
4.  13
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8.5 and
Angles and Angle Measure
Worksheet
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