1. 1
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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6.1 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.
One degree (1º) is equivalent to a rotation of of one
revolution.
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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
Radian and Degree Measure
Classifying Angles
Quadrant 1
Quadrant 3
Quadrant 4
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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.
13. Find one positive angle and one negative angle
that are coterminal with (a) −45° and (b) 395°.
There are many such angles, depending on what multiple of 360° is
added or subtracted.
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Radian and Degree Measure
Example of Finding Coterminal Angles
You can find an angle that is coterminal to a given angle by
adding or subtracting multiples of 360º.
Ex 2:
Find one positive and one negative angle that are
coterminal to 112º.
For a positive coterminal angle, add 360º : 112º + 360º = 472º
For a negative coterminal angle, subtract 360º: 112º - 360º = -248º
15. Ex 3. Find one positive and one negative angle that is
coterminal with the angle = 30° in standard position.
Ex 4. Find one positive and one negative angle that is
coterminal with the angle = 272 in standard position.
20. 20
Radian and Degree Measure
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
21. Ex 5. Convert the degrees to radian measure.
a) 60
b) 30
c) -54
d) -118
e) 45
22. Ex 6. Convert the radians to degrees.
a)
b)
c)
d)
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2
11
18
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23. Bellwork
Convert the degrees to radian measure.
1. 30
2. -54
Convert the radians to degrees.
3.
4.
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9
11
18
25. Ex 7. Find one positive and one negative angle that is
coterminal with the angle = in standard position.
Ex 8. Find one positive and one negative angle that is
coterminal with the angle = in standard position.
7
5
3
29. A sector is a region of a circle that is bounded by two radii
and an arc of the circle. The central angle θ of a sector is
the angle formed by the two radii. There are simple
formulas for the arc length and area of a sector when the
central angle is measured in radians.
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30. A softball field forms a sector with the dimensions
shown. Find the length of the outfield fence and
the area of the field.
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31. In Exercises 33–38, use a calculator to
evaluate the trigonometric function.
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