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Radian Measure and Coterminal Angles

Radian Measure and Coterminal Angles. Take out your homework from Friday!!!. Warm-up (1:30 m). Using your “Degrees and Radians” handout from Friday, describe how you convert between degrees and radians. Converting Between Degrees and Radians. Converting Between and Radians, cont.

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Radian Measure and Coterminal Angles

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  1. Radian Measure and Coterminal Angles Take out your homework from Friday!!!

  2. Warm-up (1:30 m) • Using your “Degrees and Radians” handout from Friday, describe how you convert between degrees and radians.

  3. Converting Between Degrees and Radians

  4. Converting Between and Radians, cont

  5. Picture of Unit Circle with missing degrees and radian measures. Students fill missing measures.

  6. 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

  7. Radian Measure, cont.

  8. The Unit Circle – An 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

  9. Sketching Radians 90° 0° 180° 360° 270°

  10. Sketching Radians • Trick: Convert the fractions into decimals and use the leading coefficients of pi

  11. Example #1

  12. Example #2

  13. Example #3

  14. Example #4

  15. Your Turn:

  16. Your Turn:

  17. Your Turn:

  18. Experiment Graph and on the axes below. What do you notice?

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

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

  21. Solving for Coterminal Angles • You may need to add or subtract 2 pi more than once!!! • Trick: Add or subtract the coefficients of pi rather than the entire radian measure

  22. Examples: Find a coterminal angle between 0 and 2 pi

  23. Your Turn: Find a coterminal angle between 0 and 2 pi

  24. Group Exit Ticket • Are and coterminal? Why or why not?

  25. Exit Ticket, cont. • Multiply: • Rationalize:

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