angles – part 1
DESCRIPTION
Angles – Part 1. 1. Notation, Definitions& Measurement of Angles. 2. Coterminal, Right, Complementary, Supplementary Angles & Intro to Radians. 3. Practice Problems. Notation. Variables for angles Frequently Greek letters a (alpha) b (beta) g (gamma) Q (theta). Definitions. - PowerPoint PPT PresentationTRANSCRIPT
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Angles – Part 1
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1Notation, Definitions& Measurement of Angles
Coterminal, Right, Complementary, Supplementary Angles & Intro to Radians
Practice Problems
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Notation Variables for angles
Frequently Greek letters a (alpha) b (beta) g (gamma) Q (theta)
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Definitions Initial side
Point of origin for measuring a given angle Typically 0˚ (360˚)
Terminal Side Ending point for measuring a given angle Can be any size
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Measurement Clockwise (CW)
Negative Angle Counter-Clockwise (CCW)
Positive Angle
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www.themegallery.com
Measurement (Cont.) Degrees
May be in decimal form (72.64˚) May be in Degrees/Minutes/Seconds (25˚
43’ 37”) Minutes ( ’ ) 60’ = 1˚ Seconds ( ” ) 60” = 1’
90˚ = 89˚ 59’ 60”
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Measurement (Cont.) Radians
Similar to degrees Always measured in terms of pi (π)
360˚/0˚ = 2π 90˚ = π/2 180˚ = π 270˚ = 3 π/2
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Coterminal Angles Have the same initial and terminal sides
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Finding Coterminal Angles Add multiples of 360˚ Subtract Multiples of 360˚Example: Find 4 coterminal angles of 60˚60˚ + 360˚ = 420˚ 60˚ + 720˚ =
780˚60˚ – 360˚ = -300˚ 60˚ – 720˚ = -
660˚
Answer: 420˚, 780˚, -300˚, -660˚
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Defining Angles Right Angles measure 90˚
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Finding Complimentary Angles
For degrees: = 90˚ - Qor = 89˚ 59’ 60” – Q
Example: Find the angle complementary to 73.26˚
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Finding Complementary AnglesExample 2: Find the angle that is
complementary to 25˚ 43’ 37”.
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Finding Complementary Angles For Radians
= π/2 – QExample: Find the complementary angle of
π/4 radians.
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42
44242
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Finding Supplementary Angles For degrees
= 180˚ - Q For radians
= π - Q
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Practice Problems Page 409
Problems 1-8