Coterminal Angles and Radian Measure The Unit Circle

Coterminal Angles and Radian Measure

The Unit Circle – Introduction l l Circle with radius of 1 1 Revolution = 360° l l l 2 Revolutions = 720° Positive angles move counterclockwise around the circle Negative angles move clockwise around the circle

STAND UP!!!! l l Turn – 180° (clockwise) Turn +180° (counterclockwise) Turn +90° (counterclockwise) Turn – 270° (clockwise)

What did you notice?

Coterminal Angles co – terminal with, joint, or together l ending Coterminal Angles – angles that end at the same spot

Coterminal Angles, cont. l l Each positive angle has a negative coterminal angle Each negative angle has a positive coterminal angle

Coterminal Angles, cont. 70° – 20° 250° – 290°

Solving for Coterminal Angles If the angle is positive, subtract negative, add 360° from the given to the given angle.

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

Multiple Revolutions l l 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. l To find a positive coterminal angle, subtract 360° from the given angle until you end up with an angle less than 360°

Your Turn l 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° 8. 720° 9. – 200° 7. – 20°

Radian Measure l l l 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 convert radians to radians, multiply to degrees, multiply by by

Converting Between and Radians, cont Degrees → Radians → Degrees

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