A rectangle is placed inside a semicircle of radius r, with one side along the diameter. What is the largest area the rectangle can have? There are at least two ways to set up variables you can use the coordinates of the upper corner of the rectangle, or you could use the angle the arrow makes with the diameter. Here, r is a 'parameter', to be treated as a fixed constant.

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …