Re: Help with Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg112337] Re: Help with Solve
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 10 Sep 2010 04:47:24 -0400 (EDT)

```Use Reduce

eq1 = n*Sin[x] == (m*v^2)/r;
eq2 = n*Cos[x] == m*g;

cons = {m > 0, g > 0, r > 0, v > 0};

sys = Join[{eq1, eq2}, cons];

FullSimplify[Reduce[sys, x, Reals], cons] // ToRadicals

Element[C[1], Integers] &&
v == -((n^2*r^2 - g^2*m^2*r^2)^(1/4)/Sqrt[m]) &&
((x == 2*(Pi*C[1] + ArcTan[
Sqrt[1 - (2*g*m)/(g*m + n)]]) && n > g*m) ||
(2*ArcTan[Sqrt[1 - (2*g*m)/(g*m + n)]] + x ==
2*Pi*C[1] && g*m + n < 0))

Bob Hanlon

---- Eduardo  Cavazos <wayo.cavazos at gmail.com> wrote:

=============
Hello!

A newb question I'm sure... :-)

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.e. solve eq2 for 'n', substitute this into eq1, and solve the result
for 'x'. But this approach seems too "manual".

Is there a more straightforward way to carry out the problem? I tried
this:

Solve[{eq1, eq2}, x]