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Homework Help: 3rd degree taylor series

  1. May 14, 2012 #1
    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. jcsd
  3. May 15, 2012 #2
    ##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?
  4. May 15, 2012 #3


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    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.