2. Adjust slider "a" until the Arclength is twice the radius. What is the measure of the central angle?
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3. What do you think the Arclength will be when the central angle measures 3 radians? Explain.
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4. Now adjust the "Radius" slider to change the radius. Are your answers to questions 1 - 3 still true? Why or why not?
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5. Define a radian:
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6a. Adjust "a" until the Arclength created is a semicircle. What's the approximate radian measure of the central angle? What symbol do we use for this approximation?
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6b. What's the degree measure of the central angle? Write an equation that describes the relationship between the radian and degree measure of the central angle:
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7a. Adjust "a" until the central angle is a right angle. What's the approximate radian measure of the central angle? Write this approximation as an exact value.
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7b. Write an equation that describes the relationship between the radian and degree measure of a right angle:
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8. Now use the "Radius" slider to adjust the radius. Are the relationships you discovered in questions 6 and 7 still true? Why or why not?
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9. How would you determine the exact radian measure of a 45-degree angle? 30-degree angle? How would you determine the degree measure of an angle that is (7*pi)/12 radians?
