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Radian Measure and Coterminal Angles Take out your homework from Friday!!! Warm-up (1:30 m) Using your “Degrees and Radians” handout from Friday, describe how you convert between degrees and radians. 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 220 Radians → Degrees π 5 Picture of Unit Circle with missing degrees and radian measures. Students fill missing measures. Radian Measure 180 radian 57.3 π 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. The Unit Circle – An 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 Sketching Radians 90° 0° 180° 360° 270° Sketching Radians Trick: Convert the fractions into decimals and use the leading coefficients of pi π 2 π 3π 2 2π 5π Example #1 6 6π Example #2 4 π Example #3 4 9π Example #4 7 Your Turn: 12π 7 π 3 Your Turn: 10π 7 5π 3 Your Turn: 15π 13 17π 9 Experiment Graph 3 and 2 2 do you notice? on the axes below. What Coterminal Angles co – terminal with, joint, or together ending Coterminal Angles – angles that end at the same spot Coterminal Angles, cont. Each positive angle has a negative coterminal angle Each negative angle has a positive coterminal angle Solving for Coterminal Angles If the angle is If the angle is less greater than 2 pi, than 0, add 2 pi subtract 2 pi to the given from the given angle. angle. You may need to add or subtract 2 pi more than once!!! Trick: Add or subtract the coefficients of pi rather than the entire radian measure Examples: Find a coterminal angle between 0 and 2 pi 2π 3 29π 6 Your Turn: Find a coterminal angle between 0 and 2 pi 14π 13 18π 5 9π 4 6π 4 Group Exit Ticket 7 π 17 π Are and coterminal? Why or 6 6 why not? Exit Ticket, cont. 1. 2. Multiply: 2 * 18 Rationalize: 2 2