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

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’

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

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)

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

EXAMPLEFind ϴ’ if ϴ = 210°

210° - 180° = 30°= ϴ’

Find ϴ’ if ϴ = 7π/67π/6 - π = π/6 = ϴ’

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

EXAMPLEFind ϴ’ if ϴ = 300°

360° - 300° = 60° = ϴ’

Find ϴ’ if ϴ = 5π/3

2π - 5π/3 = π/3 = ϴ’