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 "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