Question

Draw graph and contour map for

\(Z = \sin \left( {x - y} \right)\)

Short answer

Answer is not given in the drive

Step-by-step solution

Since the function\(\sin \left( {x - y} \right)\)is periodic whose value range from\( - 1{\rm{ to 1}}\), this function represents a surface that looks like tidal waves.

So, graphs are:

Contour map

Defining level curves

\(f\left( {x,y} \right) = k\),\(k\)is constant.

So, \({\rm{sin}}\left( {x - y} \right) = K\)consists of infinitely many parallel lines.

Example:\({\rm{sin}}\left( {x - y} \right) = \frac{1}{2}\). This is satisfied when:\(\left( {x - y} \right) = \frac{\pi }{6},\frac{{5\pi }}{6},\frac{{13\pi }}{6}............\)

So, the surface of the function which is almost flatter to\(xy\)place, it means that surface will be somewhat flatter near origin.

So, the contour lines are as follows: