Re: Solve can solve it with some help

*To*: mathgroup at smc.vnet.net*Subject*: [mg115396] Re: Solve can solve it with some help*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Mon, 10 Jan 2011 02:36:24 -0500 (EST)*References*: <igbnk8$hj9$1@smc.vnet.net>

Hi Eduardo, You may ask Solve to eliminate vf in the process of solving for Theta: s = {0 == 1/2*m*vf^2 + 0 - m*g*(R - R*Cos[\[Theta]]), m*vf^2/R == m*g*Cos[\[Theta]]}; Solve[s, \[Theta], vf] During evaluation of In[91]:= Solve::bdomv: Warning: vf is not a valid domain specification. Mathematica is assuming it is a variable to eliminate. >> During evaluation of In[91]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >> Out[92]= {{\[Theta] -> -ArcCos[2/3]}, {\[Theta] -> ArcCos[2/3]}} Cheers -- Sjoerd On Jan 9, 8:20 am, Eduardo Cavazos <wayo.cava... at gmail.com> wrote: > Hello, > > Solve doesn't come up with anything for these two equations: > > { > 0 == 1/2*m*vf^2 + 0 - m*g*(R - R*Cos[\[Theta]]), > > m*vf^2/R == m*g*Cos[\[Theta]] > }; > Solve[%, \[Theta]] > > If you manually solve one of them for vf, Solve can take care of the > rest: > > 0 == 1/2*m*vf^2 + 0 - m*g*(R - R*Cos[\[Theta]]); > % /. Solve[m*vf^2/R == m*g*Cos[\[Theta]], vf][[2]]; > Solve[%, \[Theta]] > > {{\[Theta] -> -ArcCos[2/3]}, {\[Theta] -> ArcCos[2/3]}} > > Of course, Reduce can handle the original set. However, Solve is nice > due to the brevity of output. (Side question: is there a way to extract > an equation from the results of Reduce based on variable name? Sometimes > the results from Reduce can be so verbose, it'd be nice to say "extract > equation for theta".) > > My main question: is there a way to get Solve to solve the original set > of two equations without taking the manual approach? > > Ed