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Coterminal Angles and Radian Measure

Coterminal Angles and Radian Measure. 11 April 2011. The Unit Circle – Introduction. Circle with radius of 1 1 Revolution = 360° 2 Revolutions = 720° Positive angles move counterclockwise around the circle Negative angles move clockwise around the circle. STAND UP!!!!.

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Coterminal Angles and Radian Measure

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  1. Coterminal Angles and Radian Measure 11 April 2011

  2. The Unit Circle – Introduction • Circle with radius of 1 • 1 Revolution = 360° • 2 Revolutions = 720° • Positive angles move counterclockwise around the circle • Negative angles move clockwise around the circle

  3. STAND UP!!!! • Turn –180° (clockwise) • Turn +180° (counterclockwise) • Turn +90° (counterclockwise) • Turn –270° (clockwise)

  4. What did you notice?

  5. Coterminal Angles co – terminal • Coterminal Angles – angles that end at the same spot with, joint, or together ending

  6. Coterminal Angles, cont. • Each positive angle has a negative coterminal angle • Each negative angle has a positive coterminal angle

  7. Coterminal Angles, cont. –20° –290° 70° 250°

  8. Solving for Coterminal Angles

  9. Your Turn

  10. Multiple Revolutions • Sometimes objects travel more than 360° • In those cases, we try to find a smaller, coterminal angle with which is easier to work

  11. Multiple Revolutions, cont. • To find a positive coterminal angle, subtract 360° from the given angle until you end up with an angle less than 360°

  12. Your Turn • For the following angles, find a positive coterminal angle that is less than 360°: 1. 570° 2. 960° 3. 1620° 4. 895°

  13. Your Turn, cont. 5. 45° 6. 250° 7. –20° 8. 720° 9. –200°

  14. Radian Measure • Another way of measuring angles • Convenient because major measurements of a circle (circumference, area, etc.) are involve pi • Radians result in easier numbers to use

  15. Radian Measure, cont.

  16. Converting Between Degrees and Radians

  17. Converting Between and Radians, cont

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