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

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The discussion centers on finding the Maclaurin series for sin(x) and simplifying it to determine the correct answer from multiple choices. The initial series derived is π/10 - π^3/6,000, but the poster struggles with simplification without a calculator. It is suggested that estimating π and π^2 can help clarify the answer, which is identified as C. 31/100 π. The conversation emphasizes the importance of using approximations to confirm the correctness of the answer choice.
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Homework Statement



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Homework Equations



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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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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