Approximating sin(1/10) using 3rd degree Taylor polynomial

[bfusco]

Homework Statement

what is the 3rd degree taylor series of sin(1/10), and calculate the error of your answer.

the wording of this question may be a little off, i just took a test and this was what i remembered about the question.

The Attempt at a Solution

i didnt think that this was possible because sin(1/10) is a constant, so the derivative is 0, therefor when you write out the taylor series expansion f(a)+f'(a)(x-a)/n!... is simply sin(1/10) and the error ofcourse would be 0, but I am guessing I am wrong because of my uncertainty.

 

[scurty]

$f'(a)$ is telling you to evaluate $f'(x)$ at $a$. Not to take the derivate of $f(a)$.

So, $f'(1/10) = \cos{(1/10)}$

Does that help clear it up?

 

[vela]

Homework Statement

what is the 3rd degree taylor series of sin(1/10), and calculate the error of your answer.

the wording of this question may be a little off, i just took a test and this was what i remembered about the question.

The Attempt at a Solution

I didn't think that this was possible because sin(1/10) is a constant, so the derivative is 0, therefore, when you write out the taylor series expansion f(a)+f'(a)(x-a)/n!... is simply sin(1/10) and the error, of course, would be 0, but I'm guessing I'm wrong because of my uncertainty.

If the problem is worded as you've given it above, then your answer is correct, but it's more likely the problem was asking you to approximate sin(1/10) using a third-order Taylor polynomial.