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