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Finding x-intercepts of epicycloid

Posted 11 years ago
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:
POSTED BY: Bryan Lettner
4 Replies
Posted 11 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 BY: David Keith
Posted 11 years ago
thank you both very much!  i will spikey in the future
POSTED BY: Bryan Lettner
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 BY: Michael Rogers
Posted 11 years ago
Hi Bryan,
Try FindInstance.

PS. 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, #]}] & /@

Show[plot1, Epilog -> points];
POSTED BY: David Keith
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