Coterminal Angles and Radian Measure

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!!!! Turn –180° (clockwise) Turn +180° (counterclockwise)

Turn +90° (counterclockwise) Turn –270° (clockwise)

What did you notice?

Coterminal Angles

co – terminal

Coterminal Angles – angles that end at the same spot

with, joint, or together

ending

Coterminal Angles, cont.

Each positive angle has a negative coterminal angle

Each negative angle has a positive coterminal angle

Coterminal Angles, cont.

70°

250°

–20°

–290°

Solving for Coterminal Angles

If the angle is positive, subtract

360° from the given angle.

If the angle is negative, add 360° to the given angle.

Your Turn

Find a negative coterminal angle of the following:

Find a positive coterminal angle of the following:

110° 270° –30° –240°

45° 315° –180° –330°

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

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°

75360435

435360795

Your Turn

For the following angles, find a positive coterminal angle that is less than 360°:

1. 570° 2. 960°

3. 1620° 4. 895°

Your Turn, cont.

5. 45° 6. 250° 7. –20°

8. 720° 9. –200°

Radian Measure

3.57180

radian

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

Radian Measure, cont.

Converting Between Degrees and Radians

To convert degrees to radians, multiply by

To convert radians to degrees, multiply by

180

180

Converting Between and Radians, cont

Degrees → Radians Radians → Degrees

2205

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.