Radian Measure of a Circle

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## Radian Measure of a Circle

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**Radian Measure of a Circle**another way to measure angles!**Opener:**• What is the circumference of a tire with a radius of 18”? • How many complete revolutions does the tire make over 1000 feet?**Measuring Angles and Arcs**• An object has been chosen for you. • You will be working as a group. • Choose a member to do a specific job: measurer(2), recorder, calculator.**Measuring Circular Objects**• While someone holds the object, measure the diameter to the nearest 1/8 of an inch. The most accurate measurement can be obtained by securing one end and moving the other to get the largest measurement as the diameter is the chord of greatest length.**Measuring Circular Objects**• Once the diameter has been obtained, determine the radius of the object (without measuring). • Afterwards, we will use our tape measure to determine the circumference of the object. What is circumference a measure of???**Measuring Circular Objects**• Hold the end securely and wrap the tape measure around the object to measure circumference. Once again measure to the nearest 1/8 of an inch. • Record this measurement.**Measuring Circular Objects**• Use the radius you calculated earlier to determine how many radii will fit around the outside of the object. • Record your answer. This number correlates to the “radians” in a circle.**Measuring Circular Objects**• Divide the number of radii that fit around your object by π. Record you answer to three decimal places. • Compare your answer with those from the groups around you. Are they the same? Should they be?**Measuring Circular Objects**• How many radii would it take to fit half way around your object? • You and your group need to come up with an explanation of what π represents and record your answer.**Measuring Circular Objects**• How many radii does it take to fit around the entire object? Divide by π to determine how many radii in terms of π. How many degrees is it all the way around the object? • Come up with a conversion factor to convert from degrees to radians using π.**How to convert from …**• Degrees to Radians: • Radians to Degrees:**Convert 235 degrees to radians:**235°{————}= radians**State your answer in terms of π!**If you walk around a circular track with a radius of 100m a total of eight times, how many radians will you have traveled? What if the radius of the track were 1000m instead of 100m?**This is why we don’t state distances in terms of**radians!!! Radians are measures of angles and arcs and are used in lieu of degrees. We often see fractional portions of π referring to angles. What do the following radian measures refer to in terms of degrees?**Tonight’s**Homework