Finding the Solution to a Maclaurin Series for Sin(x)

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Homework Help Overview

The discussion revolves around finding the Maclaurin series for sin(x) and simplifying it to determine a specific value. The original poster presents an attempt at a solution involving a series expansion and expresses difficulty in simplifying the result.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of approximations for π and π² to estimate terms in the series. Questions arise regarding the validity of the answer choices and how to confirm the correctness of a specific answer.

Discussion Status

The discussion is ongoing, with participants exploring different methods of estimation and questioning the reliability of the approximations used. Some guidance has been offered regarding how to approach the simplification of the series.

Contextual Notes

There is mention of constraints related to avoiding calculators and the need for simplification without additional tools. Participants are also considering the implications of their approximations on the final answer choices.

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Homework Statement



Problem is attached in this post.

Homework Equations



Problem is attached in this post.

The Attempt at a Solution



I used the Maclaurin Series for sin (x) and got the following series:

π/10 - π^3/6,000 + ... etc.

I can't find a way to simplify the series to get an answer (Without a calculator etc.)

The answer is C. 31/100
 

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π is about 3.14 and π2 is roughly 10. That should be sufficient, and you can make a very rough estimate for π in the second term.
 
mfb said:
π is about 3.14 and π2 is roughly 10. That should be sufficient, and you can make a very rough estimate for π in the second term.

That's true, but then some of the other answer choices could also be possible answers then, how can you say for sure then that 31/100 is the correct answer?
 
Just plug in the approximations I suggested, get your expansion on a common fraction and it will be clear.
 

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