How to find more solutions for an periodical equation with infinity solutions

*To*: mathgroup at smc.vnet.net*Subject*: [mg122900] How to find more solutions for an periodical equation with infinity solutions*From*: Gy Peng <hitphyopt at gmail.com>*Date*: Tue, 15 Nov 2011 05:50:12 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Dear all, I have a matrix defined as: Matrix[{\[Alpha]_, \[Beta]_, \[Gamma]_}, \[Theta]_] := {{\[Alpha]^2 \ (1 - Cos[\[Theta]]) + Cos[\[Theta]], \[Alpha] \[Beta] (1 - Cos[\[Theta]]) - \[Gamma] Sin[\[Theta]], \[A lpha] \[Gamma] (1 - Cos[\[Theta]]) + \[Beta] Sin[\[Theta]]}, {\[Alpha] \[Beta] (1 \ - Cos[\[Theta]]) + \[Gamma] Sin[\[Theta]], \[Beta]^2 (1 - Cos[\[Theta]]) + Cos[\[Theta]], \[Beta] \[Gamma] (1 - Cos[\[Theta]]) - \[Alpha] Sin[\[Theta]]}, {\[Alpha] \[Gamma] \ (1 - Cos[\[Theta]]) - \[Beta] Sin[\[Theta]], \[Beta] \[Gamma] (1 - Cos[\[Theta]]) + \[Alpha] Sin[\[Theta]], \[Gamma]^2 (1 - Cos[\[Theta]]) + Cos[\[Theta]]}} Solve[{x, y, z} == Matrix[{0, 0, 1}, \[Theta]].{x, y, z}, \[Theta]] I know this equation is periodical and has infinity solutions. So, Mathematica only gave me only one solution: {{\[Theta] -> 0}} and show me the message: Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >> My question is, how could I see for example first 6 solution, because I know the first 5 or 6 solutions should be different and then repeat themselves periodically. What should I do to find the first 5 or 6 solutions? Thank you very much!

**Follow-Ups**:**Re: How to find more solutions for an periodical equation with infinity solutions***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>