Re: Solve Equation
- To: mathgroup at smc.vnet.net
- Subject: [mg20855] [mg20855] Re: [mg20813] Solve Equation
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Wed, 17 Nov 1999 03:41:21 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
This is not surprising since:
In[1]:=
L = 7; b = Pi/3 ; a = Pi/3*5;
In[2]:=
{L == 5 + 4Cos[a], L == 13 - 12 Cos[b], L == 10 - 3Cos[a + b]}
Out[2]=
{True, True, False}
I get the following answers using NSolve:
In[1]:=
a /: Cos[a] = (1 - t^2)/(1 + t^2); a /: Sin[a] = (2t)/(1 + t^2);
In[2]:=
b /: Cos[b] = (1 - s^2)/(1 + s^2); b /: Sin[b] = (2s)/(1 + s^2);
In[3]:=
{L, Cos[a], Cos[b]} /.
NSolve[{L == 5 + 4Cos[a], L == 13 - 12 Cos[b],
L == 10 - 6TrigExpand[Cos[a + b]]}, {t, s, L}]
Out[3]=
{{27.8341 + 0. I, 5.70853, -1.23618},
{27.8341 + 0. I, 5.70853, -1.23618},
{8.94378, 0.985946, 0.338018},
{8.94378, 0.985946, 0.338018},
{5.22209, 0.055523, 0.648159},
{5.22209, 0.055523, 0.648159}}
Hence the solutions are L= 8.94378,Cos[a]= 0.985946,Cos[b]= 0.338018, and
L= 5.22209,Cos[a]= 0.055523 ,Cos[b]= 0.648159. Solve also gives solutions
but they look very complicated.
But then parhaps your equations were wrong. Replacing 3 by 6 in the last one
gives the answer you wanted:
In[4]:=
{L, Cos[a], Cos[b]} /.
Solve[{L == 5 + 4Cos[a], L == 13 - 12 Cos[b],
L == 10 - 3TrigExpand[Cos[a + b]]}, {t, s, L}]
Out[4]=
1 1 1 1 1 1
{{7, -, -}, {7, -, -}, {9, 1, -}, {9, 1, -}}
2 2 2 2 3 3
--
> From: "Mecit Yaman" <mecit at iname.com>
To: mathgroup at smc.vnet.net
> Date: Sun, 14 Nov 1999 18:14:01 -0500 (EST)
> To: mathgroup at smc.vnet.net
> Subject: [mg20855] [mg20855] [mg20813] Solve Equation
>
> 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
>
> Good work , everyone.
> Mecit
> MSc student @ University of Cape Town
>
>
>
>