Here is the motivation for my question. I want to plot sin(x) over the interval 0 to 2 pi, with the part from pi/2 to 2 pi as a dashed curve. I want to plot this with a legend so that it shows the solid part is for acute angles, and the dashed part is for, say, other angles. Perhaps using Show and ShowLegend will work, but I couldn't figure out how to get the legend boxes to match the curves (solid and dashed curves). It seems PlotLegend takes care of this for you, but I couldn't figure out how to use this in Show. So I thought using PlotLegend in Plot will be easiest, except I don't know how to use Plot for the same function with different options on different intervals.
I tried using the suggestions from "Plotting piecewise function with distinct colors in each section", but I think my problem is that the same function is being used for both parts of the piecewise function I defined.