Dgdrxrt

This is the problem below:

For each function given below in (i)-(iii), perform the following steps in Mathematica

Plot several level curves f(x, y) = c for c = −2, −1, 0, 1, 2, using ContourPlot.

(i) f(x, y) = sin x − cos y

Once I know how to do this, I'll be able to figure out the rest. However, this is my code and it is not working:

ContourPlot[ Sin[x] - Cos[y] == -2, x, -10, 10, y, -10, 10]

My professor has the same thing in her code, but mine is not showing anything but a blank white box. Once I know how to do that, I just need to know how to plot multiple ones together. I have tried to search, but could not find anything to help. Thank you.

Consider that $sin theta ge -1$ and $cos theta ge -1$ for all $theta$. The plot of
$$cos x - sin y = -2$$
consists of a grid of points where $x = (2k+1)pi$ and $y=(2l+frac12)pi$ for integers $k,l$. It's normal that you don't see anything. Try a value strictly between $-2$ and $2$.

The reason you are not seeing any contours is that the solutions of $$f(x,y)=sin x - cos y=2$$ or $$f(x,y)=sin x - cos y=-2$$

are isolated points in the $xy-$plane.

Try this code, and you'll see a periodic pattern:

c=Range[-2,2]/1.05;
f[x_,y_]:=Sin[x]-Cos[y];
ContourPlot[f[x,y]==c,x,-10,10,y,-10,10]

This will produce a more colorful plot:

Show@Table[ContourPlot[f[x,y]==c,x,-10,10,y,-10,10,
 ColorFunction->Function[x,y,Hue[3 c]]],c,Range[-2,2]/1.05]

If you just ask for contours, and not specify which contour, then ContourPlot[] chooses the contours (you can control how many contours to show, the colors, and other aspects of the plot (please see the documentation)). In Mathematica, putting your cursor over the plot will reveal the values of the contours.

f[x_, y_] := Sin[x] - Cos[y];
ContourPlot[f[x, y], x, -10, 10, y, -10, 10]

You can even combine two (or more) of these (if you like) with Show[]!