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Question: Why does time to plot csc(k*x) vary so widely with the value of k?

Question:Why does time to plot csc(k*x) vary so widely with the value of k?

diemer 30 Maple
plot
August 04 2010
2

When I plot csc(k*x) for various values of k, the timing varies considerably depending on the value of k.

Here are the timings for k = 1..5 (note the strange case of k = 3):

  seq(time(plot(csc(k*x), x = 0 .. 2*Pi, -3 .. 3, discont = true)), k = 1 .. 5);
               0.031, 0.031, 14.133, 0.046, 0.062

For k = 6, the time is apalling:

> time(plot(csc(6*x), x = 0 .. 2*Pi, -3 .. 3, discont = true));
                             87.220

I'm running Maple 14 on a Windows 7 box.  The results are independent of the interface (standard, classic, or command-line).

I have similar problems plotting cot(k*x).  Oddly, sec(k*x) gives no irregularities.
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