I am currently stuck on the following problem in a Calculus BC online course that I am taking while still in high school.
The first part : The Derivative Form of the Remainder for the Taylor series of f(x) will be denoted by Rsubk(x). Express Rsub5(6) in terms of the value c for the Taylor series for f(x) = sin x when sin x is expanded about a = 0.
The second part : Use the Derivative Form of the Remainder Rsubk(x) to determine the degree of the Taylor polynomial that approximates sin 6 to within 0.0005 of its actual value.
Any help whatsoever would be amazing.
I have been told that the series for f(x)=sin(x) at a=0 is equal to
tsub(2k+1)(x)= sigma (i=0 to k) of (((-1)^i)/(2i+1)!)*(x^(2i+1))
But where to go from here?