# 3rd degree taylor series

1. May 14, 2012

### bfusco

1. The problem statement, all variables and given/known data
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.

3. 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 im guessing im wrong because of my uncertainty.

2. May 15, 2012

### 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?

3. May 15, 2012

### vela

Staff Emeritus
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.