Question

Hello,

I am learning about Taylor series in school, but they are quite confusing..
Can you please explain how I should do this problem? Thank you very much!

What is the Taylor polynomial of order 5 approximation to sin(1.5) ?
I know the series of sinx = x - ((x^3)/(3!)) + ((x^5)/(5!))-...+...

but where do i go from here?

THANK YOU~

Answer 1

If
"I know the series of sinx = x - ((x^3)/(3!)) + ((x^5)/(5!))-...+..."
this is given, you only have to substitute 1.5(in radians) as x into the above series up to x^5 as requested.

For example:
sin(1.5)=1.5-1.5^3/3!+...

However, in practice, I would not stop at order 5 because the error is excessive for this value of x.