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Published byDeonte Whitham Modified about 1 year ago

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Radian Measure and Coterminal Angles Take out your homework from Friday!!!

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Warm-up (1:30 m) Using your “Degrees and Radians” handout from Friday, describe how you convert between degrees and radians.

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Converting Between Degrees and Radians To convert degrees to radians, multiply by To convert radians to degrees, multiply by

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Converting Between and Radians, cont Degrees → RadiansRadians → Degrees

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Picture of Unit Circle with missing degrees and radian measures. Students fill missing measures.

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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

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Radian Measure, cont.

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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

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0° 90° 180° 270° 360° Sketching Radians

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Trick: Convert the fractions into decimals and use the leading coefficients of pi

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Example #1

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Example #2

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Example #3

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Example #4

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Your Turn:

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Experiment Graph and on the axes below. What do you notice?

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

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

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Solving for Coterminal Angles If the angle is greater than 2 pi, subtract 2 pi from the given angle. If the angle is less than 0, add 2 pi to the given 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

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Examples: Find a coterminal angle between 0 and 2 pi

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Your Turn: Find a coterminal angle between 0 and 2 pi

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Group Exit Ticket Are and coterminal? Why or why not?

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Exit Ticket, cont. 1. Multiply: 2. Rationalize:

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