Re: Extensive replacement of trigonometric functions

• To: mathgroup at smc.vnet.net
• Subject: [mg125100] Re: Extensive replacement of trigonometric functions
• From: Mauro <pippo at hotmail.com>
• Date: Tue, 21 Feb 2012 06:15:30 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jhldmn\$ouo\$1@smc.vnet.net> <jho299\$5u6\$1@smc.vnet.net>

```Thank you, Andr=E9s.
Your suggestion is undoubtfully useful for my immediate need of formula
visualization, but -more generally- I was looking for a way to direct
Mathematica transformations toward some specific desired functions. For
example, in this case I would like that simplification process produces
Cos functions rather than Sin functions in order to recognize
similarities with other expressions. In this case, whenever I try to
elaborate an expression such Cos[\[Theta] + \[Alpha]] with \[Alpha]
number strictly greater than \[Pi]/4, it will convert to
Sin[\[Pi]/2-\[Alpha] - \[Theta]], and I want to avoid this.
Anyway, your suggestion is useful, so thank you indeed.

Mauro

Il 18/02/2012 12:32, andres ha scritto:
> So, you don't want Mathematica to evaluate the expression -Cos[\
> [Theta] + (2 \[Pi])/3]?
> Since -Cos[\[Theta] + (2 \[Pi])/3] = Sin[\[Theta] + \[Pi]/6], I assume
> you want to format the output for visualization purposes, because both
> expressions will give the same results. If this is the case, I would
> take two approaches: either apply a Hold to the rhs of the rule, or
> I'd use a rule of the type Sin[\[Theta]_ + \[Pi]/6] :>  -cos[\[Theta] +
> (2 \[Pi])/3], so that the inexistent function "cos" keeps unevaluated.
> If then you want to evaluate the expression you can release the Hold
> or define cos[\[Theta]_] := Cos[\[Theta]].
> Hope it helps.
> Andr=E9s
>
>
>
> On Feb 17, 6:29 am, Mauro<pi... at hotmail.com>  wrote:
>> Hello to everybody.
>>
>> I have this problem: I would like to replace in a long expression all
>> the occurrences of:
>>
>> Sin[\[Theta]_ + \[Pi]/6] and Sin[\[Theta]_ - \[Pi]/6]
>>
>> with respectively:
>>
>> -Cos[\[Theta] + (2 \[Pi])/3] and Cos[\[Theta] - (2 \[Pi])/3]
>>
>> (which actually are the same thing).
>> Regretfully, the application of the rules:
>>
>> Sin[\[Theta]_ + \[Pi]/6] ->  -Cos[\[Theta] + (2 \[Pi])/3]
>> Sin[\[Theta]_ - \[Pi]/6] ->  Cos[\[Theta] - (2 \[Pi])/3]
>>
>> results in a flop, since sine functions stubbornly appear again!
>>
>> Can you help me?
>>