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Angles – Part 1

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.

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Angles – Part 1

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  1. Angles – Part 1 1 Notation, Definitions& Measurement of Angles 2 Coterminal, Right, Complementary, Supplementary Angles & Intro to Radians 3 Practice Problems

  2. Notation • Variables for angles • Frequently Greek letters • a (alpha) • b (beta) • g (gamma) • Q (theta)

  3. 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

  4. Measurement • Clockwise (CW) • Negative Angle • Counter-Clockwise (CCW) • Positive Angle

  5. 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” www.themegallery.com

  6. Measurement (Cont.) • Radians • Similar to degrees • Always measured in terms of pi (π) • 360˚/0˚ = 2π • 90˚ = π/2 • 180˚ = π • 270˚ = 3π/2

  7. Coterminal Angles • Have the same initial and terminal sides

  8. 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˚

  9. Defining Angles • Right Angles measure 90˚

  10. Finding Complimentary Angles • For degrees: • = 90˚ - Q or • = 89˚ 59’ 60” – Q Example: Find the angle complementary to 73.26˚

  11. Finding Complementary Angles Example 2: Find the angle that is complementary to 25˚ 43’ 37”.

  12. Finding Complementary Angles • For Radians • = π/2 – Q Example: Find the complementary angle of π/4 radians.

  13. Finding Supplementary Angles • For degrees • = 180˚ - Q • For radians • = π - Q

  14. Practice Problems • Page 409 Problems 1-8

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