Re: Help with Solve

*To*: mathgroup at smc.vnet.net*Subject*: [mg112384] Re: Help with Solve*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 12 Sep 2010 03:11:20 -0400 (EDT)

eq1 = n*Sin[x] == (m*v^2)/r; eq2 = n*Cos[x] == m*g; soln = Simplify[ Solve[{eq1, eq2}, {x, n}][[{1, -1}]]] // Quiet {{n -> -((m*Sqrt[g^2*r^2 + v^4])/r), x -> -ArcCos[-((g*r)/Sqrt[g^2*r^2 + v^4])]}, {n -> (m*Sqrt[g^2*r^2 + v^4])/r, x -> ArcCos[(g*r)/Sqrt[g^2*r^2 + v^4]]}} Simplify[{eq1, eq2} /. soln, Element[{m, g, r, v}, Reals]] {{True, True}, {True, True}} Bob Hanlon ---- Eduardo Cavazos <wayo.cavazos at gmail.com> wrote: ============= On Sep 9, 3:23 am, Eduardo Cavazos <wayo.cava... at gmail.com> wrote: > Here's a couple of equations: > > eq1 = n*Sin[x] == (m*v^2)/r; > eq2 = n*Cos[x] == m*g; > > The goal is to solve for 'x'. > > I can do this in a roundabout way via: > > Solve[eq1 /. Solve[eq2, n], x] I should point out that the answer that I get from using Solve this way is: {{x -> ArcTan[v^2/(g r)]}} which is form the answer I'm looking for. :-) Again, I'm just wondering if Mathematica can do the work for me, instead of having to manually eliminate 'n' in a separate step. Sjoerd and Bob recommended using Reduce. Thanks for the tip! I tried to use Reduce but the results it produced were not in the above form. Ed