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Quarter 4 for Dummies Sect. 13.3 Finding reference angles

This guide explains reference angles, which are acute angles formed by the terminal side of an angle and the x-axis, denoted by Theta Prime (ϴ’). The article details how to find reference angles in different quadrants of the unit circle. For angles between 90° and 180°, subtract the original angle from 180°. For angles between 180° and 270°, subtract 180°. For angles between 270° and 360°, subtract the original angle from 360°. Examples are provided for both degree and radian measures.

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Quarter 4 for Dummies Sect. 13.3 Finding reference angles

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  1. Quarter 4 for DummiesSect. 13.3Finding reference angles Audrey Graves and Colton Brown

  2. What is a reference angle? • A reference angle is an acute angle formed by terminal side and the x-axis denoted by Theta Prime. (ϴ’) ϴ ϴ’

  3. 90° to 180° • If your original angle is between 90 degrees and 180 degrees, you take your original angle and subtract that from 180 degrees. DEGREESRADIANS ϴ =90° to 180°π/2 to π ϴ’= 180°- ϴπ+ ϴ

  4. Example • Find ϴ’ if ϴ = 120° 180° - 120° = 60° = ϴ’(you will always have an acute angle) • Find ϴ’ if ϴ = 2π/3 π - 2π/3 = π/3 = ϴ’(if your problems are given to you in radians you must give the answer in radians)

  5. 180° to 270° • If your original angle is between 180° and 270°, you subtract 180° from your original angle. DEGREESRADIANS ϴ =180° to 270°πto 3π/2 ϴ’= ϴ - 180°ϴ - π

  6. Example • Find ϴ’ if ϴ = 210° 210° - 180° = 30°= ϴ’ • Find ϴ’ if ϴ = 7π/6 7π/6 - π = π/6 = ϴ’

  7. 270° to 360° • If the original angle is between 270° to 360°, take 360° minus your original angle. DEGREESRADIANS ϴ =270° to 360° 3π/2 to 2π ϴ’=360° - ϴ2π - ϴ

  8. Example • Find ϴ’ if ϴ = 300° 360° - 300° = 60° = ϴ’ • Find ϴ’ if ϴ = 5π/3 2π - 5π/3 = π/3 = ϴ’

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