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Standards/Math/Northern Mariana Islands/HSG.C.B.5

HSG.C.B.5

HSG.C.B Find arc lengths and areas of sectors of circles
HSG.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.

Example Problems
Convert the angle θ=−30∘ to radians.
Express your answer exactly.
Convert the angle θ=72° to radians.
Express your answer exactly.
Convert the angle θ=15° to radians.
Express your answer exactly.
Khan Academy Resources
Deriving the area of a sectorArcs, ratios, and radiansChallenge problems: Arc length 1Challenge problems: Arc length 2Challenge problems: Arc length (radians) 2Challenge problems: Arc length (radians) 1Radians & degreesArc measure with equationsArc measureRadians & arc lengthRadians to degreesDegrees to radiansRadians & degreesIntro to radiansArc length from subtended angle: radiansFinding arc measures with equationsArea of a sectorRadians as ratio of arc length to radiusSubtended angle from arc lengthIntro to arc measureArc length from subtended angleArc length as fraction of circumferenceFinding arc measures
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