IA2.GR.C.8: Apply similarity to develop and use formulas involving arc length, radian measure, and sector area. a. Explain and demonstrate, using similarity, that arc length is proportional to the radius of a circle. b. Calculate the radian measure of a central angle as the ratio of arc length to radius. c. Apply the formula for the area of a sector using radian measure.

Apply similarity to develop and use formulas involving arc length, radian measure, and sector area. a. Explain and demonstrate, using similarity, that arc length is proportional to the radius of a circle. b. Calculate the radian measure of a central angle as the ratio of arc length to radius. c. Apply the formula for the area of a sector using radian measure.

Example Problems

Convert the angle

\theta = -30^\circ

to radians.
Express your answer exactly.

Convert the angle

\theta = 72\degree

to radians.
Express your answer exactly.

Convert the angle

\theta = 15\degree

to radians.
Express your answer exactly.

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