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

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Presentation on theme: "Radian Measure and Coterminal Angles Take out your homework from Friday!!!"— Presentation transcript:

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 To convert degrees to radians, multiply by To convert radians to degrees, multiply by

4 Converting Between and Radians, cont Degrees → RadiansRadians → Degrees

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

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7 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

8 Radian Measure, cont.

9 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

10 0° 90° 180° 270° 360° Sketching Radians

11 Trick: Convert the fractions into decimals and use the leading coefficients of pi

12 Example #1

13 Example #2

14 Example #3

15 Example #4

16 Your Turn:

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

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

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

22 Solving for Coterminal Angles If the angle is greater than 2 pi, subtract 2 pi from the given angle. If the angle is less than 0, add 2 pi to the given angle. 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

23 Examples: Find a coterminal angle between 0 and 2 pi

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

25 Group Exit Ticket Are and coterminal? Why or why not?

26 Exit Ticket, cont. 1. Multiply: 2. Rationalize:


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