       RE: Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26827] RE: [mg26803] Rewriting of Trigonometric Functions
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 25 Jan 2001 01:13:09 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Thomas,

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

Sin[a]^2
TrigReduce[%]
Sin[a]^2
1/2*(1 - Cos[2*a])

Sin[a]Sin[b]
% // TrigReduce
Sin[a] Sin[b]
1/2*(Cos[a - b] - Cos[a + b])

David Park

> From: Thomas Engelhardt [mailto:thomas-a.engelhardt at t-online.de]
To: mathgroup at smc.vnet.net
> 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?
>
>
> Kind Regards
>
> Thomas
> Munich, Germany
>
>
>

```

• Prev by Date: Re: triangles in circles
• Next by Date: Re: Rewriting of Trigonometric Functions
• Previous by thread: Re: Rewriting of Trigonometric Functions
• Next by thread: Re: Rewriting of Trigonometric Functions