sec 6.1 angle measure objectives: to understand the difference between radian measure and degree...
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Sec 6.1 Angle Measure
Objectives:•To understand the difference between radian measure and degree measure.•To convert between radians and degrees.•To understand co-terminal angles and how to find them.
•To understand arc lengths and area of sectors.
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QuizNextclass
will be on this:
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Radian Measure
If a circle of radius 1 is drawn with the vertex of an angle at its center, then the measure of this angle in radians (abbreviated rad) is the length of the arc that subtends the angle.
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The circumference of the circle of radius 1 is 2π. So, a complete revolution has measure 2π rad.
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Relationship between Degrees and Radians
To convert degrees to radians, multiply by .
To convert radians to degrees, multiply by .
180 radians 1801 radian
1180
radians
180
180
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Ex 1. Convert the degrees to radian measure.
a) 60
b) 30
c) -54
d) -118
e) 45
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Ex 2. Convert the radians to degrees.
a)
b)
c)
d)
6
2
11
18
9
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Class Work
1) 30
3) 120
2)3
54)
6
180
6
180
60
180
2
3
180
150
5) 210
7) 300
46)
3
118)
6
180
7
6
180
240
180
5
3
180
330
Find the degrees or radians of each:
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We define cos as the 'x' coordinate.We define sin as the 'y' coordinate.
( , )x y
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Classwork: Worksheet: 5.1 Unit Circle Worksheet
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Angle Measure
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Angles in Standard Position
An angle is in standard position if it is drawn with its vertex at the origin and its initial side on the positive x-axis.
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Coterminal Angles
• Two angles in standard position are coterminal if their sides coincide. Which angles below are coterminal?
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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 = in standard position.
3
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Class Work
Convert from degrees to radians.1. 542. -300
Convert from radians to degrees.3.
4.
11
3
13
12
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Find one postive angle and one negative angle in standard position that are coterminal with the given angle.
5.135
6. 11
6
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Ex 5. Find an angle with measure between 0 and 360 that is coterminal with the angle of measure 1290.
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Ex 6. a) Find and angle between 0 and 2 that is coterminal with 63 .
b) Find and angle between 0 and 2 that is coterminal with .88
3
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Class Work
Find an angle between 0 and 360 that is coterminal with the given angle.
7. 361
8. 1270
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Find an angle between 0 and 2 that is coterminal with the given angle.
9.
10.
7
3
51
2
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HW #1 p.474 (1,5,7,13,15) all, (25-45) e.o.o
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