plot a multiple rule function in mathematica

Question

How can I write the code for a function (complex contour) similar to this in Mathematica:

Answer 1

I am not exactly sure what c is, but I assumed it was a number between 0 and 1 meaning the height of the incoming straight line. So maybe somehting like this would suit your needs?

c = 0.7;
t0 = ArcSin[c];
PolarPlot[If[Abs[t] < t0, Abs[Sin[t0]/Sin[t]], 1], {t, -\[Pi], \[Pi]}]