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Original Message (ID '370927') By yehuda:
note - your function is not defined for x,y=0 for the first question where the ContourPlot generates an empty graph you need to change the line to ContourPlot[f[x, y] == 1, {x, -30 Pi, 30 Pi}, {y, -45 Pi, 20 Pi}, Axes -> True] (* i.e., include the argument x,y in the call to f *) for the second question, you need to use graphics primitives yourself and actually repeat what PlotLegend does. This is a task too large to answer as a forum question yehuda