RE: Tan,Cot,Csc,etc
- To: mathgroup@smc.vnet.net
- Subject: [mg12309] RE: [mg12273] Tan,Cot,Csc,etc
- From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
- Date: Thu, 7 May 1998 18:51:51 -0400
Arturas Acus wrote:
|
|do anybody knows a simple way to get rid of functions like Tan[],
|Cot[], Csc[], and others in the output of trigonometric computations.
|I would like to keep only Sin[] and Cos[] instead. |
|For example instead Csc[a]*Cot[a] I would like to have
|Cos[a]/(Sin[a]^2) and so on.
|
I can get you part way there.
In[1]:=
Off[General::spell1]
In[2]:=
FirstRules= {Csc[x_]->1/tSin[x], Sec[x_]->1/tCos[x],
Tan[x_]->tSin[x]/tCos[x],
Cot[x_]->tCos[x]/tSin[x]};
In[3]:=
SecondRules={tSin->Sin,tCos->Cos};
In[4]:=
SinCosOnly[expr_]:=With[{new=expr//.FirstRules},
HoldForm[Evaluate[new]]//.SecondRules]
_______________________________________ Now I convert an expression to
Sin and Cos only.
In[5]:=
ex1=SinCosOnly[ Csc[x]Tan[x]+Tan[x]+Sin[x]Tan[x] ]
Out[5]=
\!\(\* TagBox[ blah, blah, blah, .....
Translated into ASC we have,
1/Cos[x]+Sin[x]/Cos[x]+Sin[x]Sin[x]/Cos[x]
Unfortunately my rule doesn't simplify (Sin[x]Sin[x]) into (Sin[x]^2).
If I worked at it I could probably crack that part, but I don't know if
I will have the time.
______________________________________ Now we don't get what we want if
we use the above result in later calculations.
In[6]:=
ex1-Tan[x]
Out[6]=
\!\(\*RowBox[{ blah, blah, blah, .....
Translated into ASC we have,
1/Cos[x]+Sin[x]/Cos[x]+Sin[x]Sin[x]/Cos[x]-Tan[x]
_____________________________________ We can use the above result if we
change HoldForm to Identity. Note: A few weeks ago I asked the group
what Identity is good for.
In[7]:=
(ex1/.HoldForm->Identity)-Tan[x]
Out[7]=
Sec[x]+Sin[x] Tan[x]
The new feature at the top of my wish list is a new type of Hold (I
call it HoldTemporary).
HoldTemporary could be used here instead of HoldForm. HoldTemporary
would work very much like HoldForm, except the hold would be removed
as soon as we try to do anything to an expression with this head.
This way we would not have to remove the Hold when we use the held
result in later calculations.
Ted Ersek