Coterminal Angles and Radian Measure

Coterminal Angles and Radian Measure 11 April 2011

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. –20° –290° 70° 250°

Solving for Coterminal Angles

Your Turn

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°

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 • 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

Converting Between and Radians, cont

Coterminal Angles and Radian Measure