angles & angle measures 33 22 11 notation, definitions& measurement of angles, coterminal,...
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Angles & Angle Measures
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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 α (alpha) β (beta) γ (gamma) θ (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˚ - θor = 89˚ 59’ 60” – θ
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 – θExample: Find the complementary angle of
π/4 radians.
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Finding Supplementary Angles For degrees
= 180˚ - θ For radians
= π - θ
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Converting Between Radians and Degrees
To Change Multiply by Example
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Converting Decimal Degrees to Degrees/Minutes/Seconds
D˚ M’ S” = D˚ + ˚ + ˚
Example: Convert 19˚ 47’ 23” to decimal degrees.
60
M
3600
S
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Converting Radians to Degrees/Minutes/Seconds
Convert radians to decimal degrees Non-decimal portion is in degrees
Multiply decimal portion by 60’ Non-decimal portion is minutes
Multiply decimal portion by 60” & round Seconds
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Converting Radians to Degrees/Minutes/Seconds (Cont.)
Example: If θ =3 radians, approximate θ in terms of degrees/minutes/seconds.
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