G.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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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