# Thread: sinx and cosx Taylor Formula

1. ## sinx and cosx Taylor Formula

Find the Taylor's formula for the given function f at a=0. Find both the Taylor polynomial of the indicated degree n and the remainder term

f(x)=sinx n=4
f(x)=cosx n=4

I thought the Taylor formula and the remainder term for f(x)=cosx n=4, was
1 - ((x^2)/2!) + ((x^4)/4!) - ((x^6)/6!) + ((x^8)/8!) - ((sinz)(x^5))/5!

However, the book tells me that the answer is 1 - ((x^2)/2!) + ((x^4)/4!) - ((sinz)(x^5))/5! . What am I doing wrong here and how should i solve f(x)=sinx n=4?

2. The Taylor expansions of $\displaystyle f(x)=\cos x$ around $\displaystyle x=0$ is...

$\displaystyle \cos x = a_{0} + a_{1}\cdot x + a_{2} \cdot x^{2} + a_{3}\cdot x^{3} + a_{4}\cdot x^{4} + R_{4} (x) =$

$\displaystyle = 1 + 0\cdot x - \frac{x^{2}}{2} + 0\cdot x^{3} + \frac{x^{4}}{24} - \frac{\sin \theta}{120} \cdot x^{5}$ (1)

... so that your book is wright!... don't forget that for the function $\displaystyle \cos x$ is $\displaystyle a_{1} = a_{3} = 0$ ...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$