Area Swept by a Segment to a Moving Point on the Unit Circle

★ 6/10plane geometry trigonometry Parametrization Circles analytic geometry

Problem

Let $A(2,0)$ be a fixed point in the plane, and let

P\left(\sin(2t-60^\circ),\ \cos(2t-60^\circ)\right)

be a moving point. As $t$ increases from $15^\circ$ to $45^\circ$ , find the area of the region swept out by the segment $AP$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, trigonometry, Parametrization, Circles, analytic geometry

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