Re: Solve Equation
- To: mathgroup at smc.vnet.net
- Subject: [mg20846] [mg20846] Re: [mg20813] Solve Equation
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Wed, 17 Nov 1999 03:41:05 -0500 (EST)
- References: <199911142314.SAA02155@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Mecit Yaman wrote:
>
> i am trying to solve 3 equations on 3 variables. Mathematica is complaining
> about trigonometric functions, sin and cosine.
>
> L= 5+4Cos[a]
> L=13-12 Cos[b]
> L=10 - 6Cos[a+b]
>
> I tried to change
> Cos[a] -> x
> Cos[b] -> y
> Cos[a+b] - > (x y - Sqrt[1-x x]Sqrt[1- y y])
>
> But this time it only gives me a trivial solution.(L=0)
> I am trying to get the solution.
>
> L=7, b=Pi/3 , a= Pi/3*5
I rather hope Solve will not give that as a result.
exprs = {5+4*Cos[a]-L, 13-12*Cos[b]-L, 10-6*Cos[a+b]-L};
In[12]:= exprs /. {L->7, b->Pi/3 , a->Pi/3*5}
Out[12]= {0, 0, -3}
The following will get you a pair of fairly concise solutions.
SetOptions[Roots, Cubics->False]
soln = Solve[exprs==0, {L,a,b}];
In[16]:= FullSimplify[{L,a,b} /. soln]
2 3
Out[16]= {{Root[-1300 + 441 #1 - 42 #1 + #1 & , 3],
2 3
> ArcCos[Root[-5 + 96 #1 - 108 #1 + 16 #1 & , 3]],
2 3
> ArcCos[Root[13 - 48 #1 + 12 #1 + 48 #1 & , 1]]},
2 3
> {Root[-1300 + 441 #1 - 42 #1 + #1 & , 2],
2 3
> ArcCos[Root[-5 + 96 #1 - 108 #1 + 16 #1 & , 2]],
2 3
> ArcCos[Root[13 - 48 #1 + 12 #1 + 48 #1 & , 2]]}}
In[17]:= N[%]
Out[17]= {{27.8341, 0. + 2.42735 I, 3.14159 - 0.674426 I},
> {8.94378, 0.167852, 1.22599}}
Daniel Lichtblau
Wolfram Research
- References:
- Solve Equation
- From: "Mecit Yaman" <mecit@iname.com>
- Solve Equation