Coterminal Angles and Radian Measure

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Presentation transcript:

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)

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

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°

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

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

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