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**Lunar** 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* = (2*x*)*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 "theta".

1) Derive the formula for the area of the inscribed rectangle as a function of theta. We refer to this function as *A*(theta) below.

*A*(theta) = ?

So I guess the area is: (2*x) * (sqrt(16-x^2))?

2) Plot *A*(theta) over its relevant domain. What is the relevant domain?

I have no idea what the domain is, is it [0, 8]?

3)For what value of theta is the maximum area attained?

4)What is the maximum area?

I know I have to take the 1st derivative, but I don't know if my area is set up right. any help is greatly appreciated