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 → Radians
Radians → Degrees

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

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

11. Sketching Radians
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:

17. Your Turn:

18. Your Turn:

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.
Multiply:
Rationalize: