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**1. The problem statement, all variables and given/known data**

What degree Taylor Polynomial around a = 0(MacLaurin) is needed to approximate cos(0.25) to 5 decimals of accuracy?

**2. Relevant equations**

taylor series....to complicated to type out here

remainder of nth degree taylor polynomial = |R(x)| <= M/(n+1)! * |x - a|^(n+1)

where a = 0 in this case

and

M >= |f^(n+1)(t)|

**3. The attempt at a solution**

I don't really get this question at all. I know that |R(0.25)| = 0.00001 <= M/(n+1)! * |x - a|^(n+1)

But how do I get M when |f^(n+1)(t)| is unknown? I don't even know what |f^(n+1)(t)| means!