Taylor approximation to cos(x) with error < 0.0001

[dopey9]

I'm trying to find the interval of which 1 - (x^2)/2 is an approximation for cos(x) with an error less than 0.0001?

I know it's got something to do with the Taylor polynomial. I've tried letting it equal each other and substituting 0.0001 but it all just cancels out. Any ideas?

 

[marcmtlca]

1-x^2/2

you are using an expansion about 0 i think here. Consider the interval [-x,x]. The error is less than twice the third term i think (because it is alternating).

this is ERROR < 2|x^3/3|
u want ERROR<0.0001

set 2x^3/3 = 0.0001

and solve

(i havent done this stuff in a while so u may want to double check this)