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QUARTER 4 FOR DUMMIESS E C T. 1 3 . 3
F I N D I N G R E F E R E N C E A N G L E SAudrey Graves and Colton Brown
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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’)
ϴϴ’
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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.
DEGREES RADIANS
ϴ =90° to 180° π/2 to πϴ’= 180°- ϴ π+ ϴ
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EXAMPLEFind ϴ’ if ϴ = 120°180° - 120° = 60° = ϴ’ (you will always have an acute angle)
Find ϴ’ if ϴ = 2π/3π - 2π/3 = π/3 = ϴ’ (if your problems are given to you in radians you must give the answer in radians)
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180° TO 270°
If your original angle is between 180° and 270°, you subtract 180° from your original angle.
DEGREES RADIANS
ϴ =180° to 270° π to 3π/2 ϴ’= ϴ - 180° ϴ - π
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EXAMPLEFind ϴ’ if ϴ = 210°
210° - 180° = 30°= ϴ’
Find ϴ’ if ϴ = 7π/67π/6 - π = π/6 = ϴ’
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270° TO 360°
If the original angle is between 270° to 360°, take 360° minus your original angle.
DEGREES RADIANS
ϴ = 270° to 360° 3π/2 to 2πϴ’= 360° - ϴ 2π - ϴ
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EXAMPLEFind ϴ’ if ϴ = 300°
360° - 300° = 60° = ϴ’
Find ϴ’ if ϴ = 5π/3
2π - 5π/3 = π/3 = ϴ’