Plot the function below.

Question

Plot the function below.

 

 

f(x,y)=sin x cos y

Answer 1

The easiest way to start this is to type "Plot sin x cos y" into wolfram alpha.

 

Note that there is a certain value for x in which sin (x) = 0 and a certain value for y in which cos(y) = 0. These values associate with two path lines that form a cross on the graph of zero height.

 

You may also want to pay close attention to the range of lines such as (t,PI) where t goes from say -5 to positive 5, because these for cross sections, which I believe could also be called level sets, in the course. You should know what something like f(4, PI) is.

 

You can use the Hessian Matrix to find local maxima and minima. It includes mixed partial derivatives.

Answer 2

You need a 3D graph; x & y are independent variables, and the third coordinate (perpendicular to the xy plane) takes on z values which are a function of the two inputs, x & y.

 

A job for Mathematica?