Question: A rectangle is inscribed in a semicircle of radius 1. See the illustration. (a) Express the area A of the rectangle as a function of

A rectangle is inscribed in a semicircle of radius 1. See the illustration.

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(a) Express the area A of the rectangle as a function of the angle θ shown in the illustration.

(b) Show that A(θ) = sin(2θ).

(c) Find the angle θ that results in the largest area A.

(d) Find the dimensions of this largest rectangle.

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