Largest rectangle inscribed in a semicircle

Determine the area of the largest rectangle that can be inscribed in a semicircle of radius 8". Figure shows that the area can be written as A =(2x)y, if (x,y) is the point of the upper right corner of the rectangle. However, we choose to parameterize the area by a single value, the angle delta.Derive the formula for the area of the inscribed rectangle as a function of delta. We refer to this function as A(delta) below.

A(delta)=?

Determine the area of the largest rectangle that can be inscribed in a semicircle of radius 8". Figure shows that the area can be written as A =(2x)y, if (x,y) is the point of the upper right corner of the rectangle. However, we choose to parameterize the area by a single value, the angle delta.Derive the formula for the area of the inscribed rectangle as a function of delta. We refer to this function as A(delta) below.

A(delta)=?

## This question was asked on May 09, 2010.

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