# Taylor series approximation to cosine

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• February 5th 2009, 04:56 PM
mr_motivator
Taylor series approximation to cosine
Use four terms of the taylor expansion for cos near 30 to calculate cos (34). Answer to 5 significant figures....
• February 5th 2009, 08:05 PM
Chris L T521
Quote:

Originally Posted by mr_motivator
Use four terms of the taylor expansion for cos near 30 to calculate cos (34). Answer to 5 significant figures....

Apply the definition of the Taylor Series:

In case of cos(x) about x=30 we see that the first 4 terms are $\cos(30)-\sin(30)\left(x-30\right)-\frac{\cos(30)}{2}\left(x-30\right)^2+\frac{\sin(30)}{6}\left(x-30\right)^3$

Now substitute x=34 into this Taylor polynomial of degree 3 and approximate it to 5 sig figs.

Can you take it from here?