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Angles and Arcs Lesson 2.1
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Angles Ray Angle Formed of two rays Have same endpoint
Extends indefinitely Ray Angle Formed of two rays Have same endpoint Endpoint
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Angles Angles can be Straight Right Acute Obtuse Obese less than 90°
greater than 90° View NSpire Demo
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Angles Positive Angles Negative Angles Measured counter-clockwise
Measured clockwise
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Angles Degree = of a full revolution Complementary angles
a + b = 90° Supplementary angles a + b = 180°
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Co-terminal Angles We measure angles in standard position on the coordinate axes This same angle could be θ
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Radian Angle Measure Consider the length of the radius laid out on the circumference The resulting angle θ, is 1 radian There are radians in a circle r θ r View NSpire Demo
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Radian Angle Measure Conversion of radians to degrees
Use this proportion Solve for desired value (degrees or radians) Try it: is how many degrees? 135° is how many radians?
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Arc Length Given a circle with radius r and central angle = θ radians
The arc length can be calculated by Try it: For a circle with radius 3.5 and θ = what is the arc length? S θ r View NSpire Demo
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Linear and Angular Speed
Angular speed is radians/unit time Linear speed is linear units / unit time
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Linear and Angular Speed
If ω is the angular velocity of a round object with radius r The linear velocity of a point on the circle is For a 20 ft radius windmill rotating at 10 rpm, what is the linear velocity of the tip of the blade?
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Assignment Lesson 2.1 Page 130 Exercises 1 – 69 EOO 71,79,83
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