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Coterminal Angles

Coterminal Angles. Two angles in standard position that share the same terminal side. Since angles differing in radian measure by multiples of 2 p, and angles differing in degree measure by 360° are equivalent, every angle has infinitely many coterminal angles. Coterminal Angles. 52°.

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Coterminal Angles

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  1. Coterminal Angles • Two angles in standard position that share the same terminal side. • Since angles differing in radian measure by multiples of 2p, and angles differing in degree measure by 360° are equivalent, every angle has infinitely many coterminal angles.

  2. Coterminal Angles 52° p/3 radians Use multiplesof 360° to find positive coterminal angles. Use multiples of 2p to find positive co- terminal angles

  3. Find one positive and one negative angle that are coterminal with an angle having a measure of 7p/4. 7p 4 15p 4 2p + = 7p 4 p 4 - 2p - =

  4. Find all angles that coterminal with a 60° angle. • Since all angles that are multiples of 360° are coterminal with a given angle, all angles coterminal with a 60° are represented by: 60° + 360k° where k is an integer.

  5. Reference Angles • A reference angle is defined as the acute angle formed by the terminal side o the given angle and the x-axis. reference angle 218° 57° 38° 128° reference angle 52° 331° reference angle 29° reference angle

  6. Find the measure of the reference angle for each angle. 13p 3 5p 3 5p 4 This angle is in Quadrant III so we must find the difference between it and the x-axis. - 2p - = 6p 3 5p 3 p 3 - = This angle is coterminal with 5p/3 in quad- rant IV, so we Must find the difference be- tween it and the X-axis. 5p 4 - p = 5p 4 4p 4 p 4 reference angle - = reference angle

  7. Find the measure of the reference angle for 510° • 510° is coterminal with 150°, which is in quadrant III, so we must find the difference between 150° and the x-axis. • 180° - 150° = 30° reference angle

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