Re: How to get the function ?

• To: mathgroup at smc.vnet.net
• Subject: [mg89372] Re: How to get the function ?
• From: Steven Siew <stevensiew2 at gmail.com>
• Date: Sat, 7 Jun 2008 03:00:00 -0400 (EDT)
• References: <g2b4ot\$nmg\$1@smc.vnet.net>

On Jun 6, 8:50 pm, Joe <Joe.Varghese.J... at gmail.com> wrote:
> Now the Qn is to rearrange the first two eq, so that I can find R
> directly..
> R = Fn( X1, Y1 )
>
> what would be the function..............
>
> Thanka a lot...
> Joe.

Mathematica 5.2 for Students: Microsoft Windows Version
Copyright 1988-2005 Wolfram Research, Inc.

In[1]:=
Out[1]= {stdout}

In[2]:= (* Write your mathematica code below *)

In[3]:= Off[Solve::verif,Solve::ifun]

In[4]:= equation01 = {x2==R Sin[theta2], y2==R(1-Cos[theta2])}

Out[4]= {x2 == R Sin[theta2], y2 == R (1 - Cos[theta2])}

In[5]:= answer02 = Reduce[x1 == R*Sin[theta1] && R == y1 +
R*Cos[theta1] && x1 > 0 && y1 > 0 && Pi/2 > theta1 > 0, R]

Pi                           theta1
Out[5]= 0 < theta1 < -- && x1 > 0 && y1 == x1 Tan[------] &&
2                              2

theta1               theta1 2
Cot[------] (x1 + x1 Tan[------] )
2                    2
>    R == ----------------------------------
2

In[6]:= equation03 = Select[answer02,MatchQ[#,Equal[y1,__]]&]

theta1
Out[6]= y1 == x1 Tan[------]
2

In[7]:= equation04 = Select[answer02,MatchQ[#,Equal[R,__]]&]

theta1               theta1 2
Cot[------] (x1 + x1 Tan[------] )
2                    2
Out[7]= R == ----------------------------------
2

In[8]:= rule04 = Rule @@ equation04

theta1               theta1 2
Cot[------] (x1 + x1 Tan[------] )
2                    2
Out[8]= R -> ----------------------------------
2

In[9]:= soln05 = Solve[equation03,theta1]

y1
Out[9]= {{theta1 -> 2 ArcTan[--]}}
x1

In[10]:= soln06 = rule04 /. soln05

2
y1
x1 (x1 + ---)
x1
Out[10]= {R -> -------------}
2 y1

In[11]:= equation07 = equation01 /. soln06

2
y1
x1 (x1 + ---) Sin[theta2]
x1
Out[11]= {x2 == -------------------------,
2 y1

2
y1
x1 (x1 + ---) (1 - Cos[theta2])
x1
>    y2 == -------------------------------}
2 y1

In[12]:= (* End of mathematica code *)

In[13]:= Quit[];

What you are looking for is

soln05  which talks about theta1 as a function of x1 and y1

soln06 which talks about R as a function of x1 and y1

Steven Siew

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