warm up for 8.5 compare the ratios sin a and cos b compare the ratios sec a and csc b compare the...
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Warm up for 8.5Warm up for 8.5
Compare the ratios sin A and cos B
Compare the ratios sec A and csc B
Compare the ratios tan A and cot B
pg 618
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?
Angle of Depression Pg 622
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Radian and Degree MeasureRadian 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
Lots of room for notes on 623
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Angles
Trigonometry: measurement of triangles
Angle Measure
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Standard Position
Vertex at origin
The initial side of an angle in standard position is always located on the positive x-axis.
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Positive and negative angles
When sketching angles, always use an arrow to show direction.
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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.
One degree (1º) is equivalent to a rotation of of one
revolution.
1
360
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Measuring Angles
1
360
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Angles are often classified according to the quadrant
in which their terminal sides lie.
Ex1: Name the quadrant in which each angle lies.
50º
208º II I
-75º III IV
Classifying Angles
Quadrant 1
Quadrant 3
Quadrant 4
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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 Measure
A second way to measure angles is in radians.
Definition of Radian:
One radian is the measure of a central angle that intercepts arc s equal in length to the radius r of the circle.
s
r
In general,
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Radian Measure
2 radians corresponds to 360
radians corresponds to 180
radians corresponds to 902
2 6.28
3.14
1.572
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Radian Measure
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Conversions Between Degrees and Radians
1. To convert degrees to radians, multiply degrees by
2. To convert radians to degrees, multiply radians by
180
180
Ex 5. Convert the degrees to radian Ex 5. Convert the degrees to radian measure.measure.
a) 60
b) 30
c) -54
d) -118
e) 45
Ex 6. Convert the radians to degrees.Ex 6. Convert the radians to degrees.
a)
b)
c)
d)
6
2
11
18
9
17
0°
360 °
30 °
45 °
60 °
330 °
315 °
300 °
120 °
135 °
150 °
240 °
225 °
210 °
180 °
90 °
270 °
Degree and Radian Form of “Special” Angles
Class WorkClass Work
Convert from degrees to radians.1.542.-300
Convert from radians to degrees.3.
4.
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3
13
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8.5 and 8.5 and Angles and Angle Measure Angles and Angle Measure
WorksheetWorksheet
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