# Finding x-intercepts of epicycloid

Posted 10 years ago
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 I am plotting an epicycloid and trying to find the x values of where the plot intercepts the x-axis.  Here's what I've done:When I solve (setting y = 0), I get an output that I don't know how to interpret:
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Posted 10 years ago
 You're welcome, Bryan.BTW, I like Michaels's use of NSolve better than my FindInstance. It seems more likely that Mathematica is commited to finding all the solutions.
Posted 10 years ago
 thank you both very much!  i will spikey in the future
Posted 10 years ago
 You can also use  NSolve,  like this,  with David Keith's setup:NSolve[ycoordinate[2/5, 46/35, t] == 0 && 0 <= t <= 46 \[Pi], {t}, Reals]
Posted 10 years ago
 Hi Bryan,Try FindInstance.Best,DavidPS. If you put your code in a spikey box we can copy/paste from it.(Remove semicolons and evaluate) xcoordinate[a_, b_, t_] := (a + b) Cos[t] - b Cos[(a + b)/b t];  ycoordinate[a_, b_, t_] := (a + b) Sin[t] - b Sin[(a + b)/b t];  plot1 = ParametricPlot[{xcoordinate[2/5, 46/35, t],      ycoordinate[2/5, 46/35, t]}, {t, 0, 46 \[Pi]}];  (* Find t for up to 1000 instances *) tValues =   t /. FindInstance[     ycoordinate[2/5, 46/35, t] == 0 && 0 <= t <= 46 \[Pi], {t},      Reals, 1000] // N;(* Make points at the intercept coordinates *)points = {Red,    Point[{xcoordinate[2/5, 46/35, #], ycoordinate[2/5, 46/35, #]}] & /@     tValues};Show[plot1, Epilog -> points];
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