1. Coterminal Angles and Radian Measure

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)

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
If the angle is positive, subtract 360° from the given angle.
If the angle is negative, add 360° from the given angle.

9. Your Turn 110° 270° –30° –240° 45° 315° –180° –330°
Find a negative coterminal angle of the following:
Find a positive coterminal angle of the following:
110°
270°
–30°
–240°
45°
315°
–180°
–330°

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°:
° °
° °

13. Your Turn, cont.
5. 45° ° 7. –20°
° 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
To convert degrees to radians, multiply by
To convert radians to degrees, multiply by

17. Converting Between and Radians, cont
Degrees → Radians
Radians → Degrees

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