Taylor Series Help: Solving sin(x) Equation

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Homework Help Overview

The discussion revolves around the Taylor Series expansion of the sine function, specifically focusing on a series representation that involves terms with powers of π. Participants are trying to identify the function represented by a given series that resembles the Taylor Series for sin(x).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the given series and the Taylor Series for sin(x). There are attempts to factor out terms and identify the function represented by the series. Questions arise about the implications of factoring and the nature of the resulting function.

Discussion Status

Some participants have provided guidance on factoring and interpreting the series, while others have expressed uncertainty about the series' identity. There is a recognition of the series' resemblance to sin(something), but no explicit consensus has been reached regarding the final form of the function.

Contextual Notes

Participants have noted difficulties in interpreting the notation used in the series, which may affect clarity in the discussion. The context suggests that the problem is part of a homework assignment, which may impose certain constraints on the discussion.

vucollegeguy
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The Taylor Series of sin(x)=x-(x3/3!)+(x5/5!)-...

What function of sin gives the following:

(\pi2/(22) - (\pi4/(24*3!)+ (\pi6/(26*5!) - (\pi8/(28*7!)+...

Please help me.
Thank you.
 
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vucollegeguy said:
The Taylor Series of sin(x)=x-(x3/3!)+(x5/5!)-...

What function of sin gives the following:

(\pi2/(22) - (\pi4/(24*3!)+ (\pi6/(26*5!) - (\pi8/(28*7!)+...

Please help me.
Thank you.
Your mix of [ tex] and [ SUP] tags makes it hard to tell what you wrote.
 
If you factor out pi/2, what do you get?
 
Thanks.
Got that factored out.

Is that my final answer?
 
No, your final answer should be something like A*sin(B). Factoring out the pi/2 should give you an idea of what function your Maclaurin series represents.
 
I don't recogize the series except that it comes from sin(something)...
 
Isn't this what you have?
\frac{\pi}{2}\left(\frac{\pi/2}{1!}~-~\frac{(\pi/2)^3}{3!}~+~\frac{(\pi/2)^5}{5!}~-~\frac{(\pi/2)^7}{7!}~...\right)

Looks pretty suggestive to me.
 
I figured it out as soon as I posted my last reply.
Thanks to you all!
 

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