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

[student93]

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

 

[mfb]

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.

 

[student93]

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?

 

[mfb]

Just plug in the approximations I suggested, get your expansion on a common fraction and it will be clear.