Reduce, Solve and FindRoot all appear to struggle with this:
a[t_] := 1 + Cos[t] + Cos[2 t]
b[t_] := Sin[t] + Sin[2 t]
c[t_] := Sqrt[(Cos[t] + 2*Cos[2*t])^2 + (-Sin[t] - 2*Sin[2*t])^2]
d[t_] := Abs[-(Derivative[1][b][t]*Derivative[2][a][t]) +
Derivative[1][a][t]*Derivative[2][b][t]]/(Derivative[1][a][t]^2 +
Derivative[1][b][t]^2)^(3/2)
Solve[c[t] == 2/d[t], t]
FindRoot[c[t] == 2/d[t], {t, 2 Pi/3}]
(*out:
{}
{t -> 2.0944}
*)
Expected result is $2\pi/3$, the real roots being periodic:
but Mathematica appears to have difficulty with Solve and Reduce and it doesn't give a closed solution for the FindRoot. Is there anything I can do to yeild the expected result?
Solve[c[t] == 2/d[t] && 0 < t < Pi, t]. You should read Can Reduce really not solve for x here?, these are also on topic How do I solve this equation? and Solve symbolically a transcendental trigonometric equation and plot its solutions – Artes Oct 24 '14 at 10:42Reals- silly me! BTW, what doesC[1]mean? – martin Oct 24 '14 at 10:46Csymbol in Mathematica for your own variables. I recommend to read carefully all the above posts, then you will find adequate details concerning your problem. – Artes Oct 24 '14 at 10:49C[1]in the docs? – martin Oct 24 '14 at 10:53Cand pressF1. – Artes Oct 24 '14 at 10:54