And, I strongly suspect that in the section where this problem is given, there is a formula for the error you get in using cutting a McLaurin or Taylor's polynomial of degree n (that is, cutting off the McLaurin or Taylor's series at the nth power). It should look something like this:
where " " is an upper bound on the absolute value of the n+1 derivative of the function.
Since this problem asked about the "9th order MacLaurin series for sin(x)" for x between -7 and 7. Okay you need . What is the 10th derivative of sin(x)? What is its largest value between -7 and 7 (radians: is about 6.28 so this is from less than to larger than ).