Re: Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26822] Re: Rewriting of Trigonometric Functions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 25 Jan 2001 01:13:05 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <94m8st\$3mn@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

strange my Mathematrica say:

In[]:=TrigReduce /@ {Sin[a]^2, Sin[a]*Sin[b]}

Out[]={(1 - Cos[2*a])/2, (Cos[a - b] - Cos[a + b])/2}

"TrigReduce[expr] rewrites products and powers of trigonometric
functions in \
expr in terms of trigonometric functions with combined arguments."

Regards
Jens

Thomas Engelhardt wrote:
>
> Dear Mathgroup members,
>
> I have just started to use Mathematica and directly ran into a problem:
>
> I have rather lengthy expressions resulting from putting a sum of two
> sinusodial swings to the power of three (Two-tone Intermodulation).
> In order for me to recognise the contained frequencies I want Mathematica to
> rewrite the contained Trigonometric functions in certain ways, namely like:
>
> [sin(a)]^2  should be transformed into 1/2*(1+cos2x)
> and for higher powers accordingly.
>
> Furthermore:
> sin(a)*sin(b) should be changed to 1/2*[cos(a-b) - cos(a+b)]
>
> I have tried all kinds of "Expand" and "Trig..." operations but Mathematica
> always keeps the powers on the trigonometric functions and doesn't change
> the multiplications either.
>
> Does anybody have an idea how I can get Mathematica to transform the
> expressions in the desired way?
>
> I appreciate your help!
> Thanks in advance.
>
> Kind Regards
>
> Thomas
> Munich, Germany

```

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