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applications and areas of math use di erent ways of measuring for di erent purposes. Here are some questions for discussion:
• “How could you use your strategy to convert 17 degrees to radians?” (Possible response: 17 degrees is of a full circle. A full circle measures radians, so 17 degrees would be
radians, which is roughly 0.30 radians.)
• “How could you use your strategy to convert 3 radians to degrees?” (Possible response: 3 radians is of a full circle. A full circle measures 360 degrees, so 3 radians would be
degrees, which is roughly 171.89 degrees.)
Lesson Synthesis
In this lesson, students have computed circumferences, arc lengths, radii, fractions of a circumference, and converted between degree and radian angle measures. Here are some questions for discussion:
• “If an angle measures degrees, what would the radian measure be?” ( radians or equivalent.)
• “If an angle measures radians, what would the degree measure be?” ( degrees or equivalent.)
• “Is there anyone who got an equivalent answer but thought about it a di erent way?” (Possible response: Each 1 degree is radians divided into 360 parts, so we can multiply the number of degrees by radians per degree to get the number of radians. So degrees would be
radians. Similarly, each 1 radian is of degrees, so radians is degrees.)
• “Suppose there is a circle with a central angle of 50 degrees and a radius of 6 meters. What is the arc length traced out by the central angle?” (Possible responses: The circumference is meters, and 50 degrees takes up or of a circle, so the arc length will be
meters, which is meters. Alternatively, 50 degrees is or radians. So the arc length is times the radius of 6 meters, which is meters.)
3.4 Radians Hidden in Degrees
Cool Down: 0 minutes
Unit 7 Lesson 3: Measure That Arc
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