The discussion focuses on finding the dimensions of the rectangle with the largest area that lies on the curve y=cos(x) and has its base on the x-axis. The area A is defined as A=2x*cos(x), where x is the x-coordinate of the rectangle's vertices. To maximize the area, the derivative of A with respect to x is taken and set to zero, leading to the transcendental equation cot(x)=x. A suggested trial solution is x=π/4, where cot(π/4)=1, indicating that further numerical methods or calculator solutions are necessary to achieve the desired precision of five decimal places.
PREREQUISITESStudents studying calculus, particularly those interested in optimization problems, as well as educators looking for examples of applying calculus to real-world scenarios involving trigonometric functions.
LogicalTime said:I'm getting a transcendental equation out of this cot(x)=x, guess you have to solve with your calculator from there unless I am making some mistake somewhere, usually these types of problems are a little cleaner to solve.