well yeah i can add up the values.
sin(1) = 0.8414709848
7 terms = 0.841468254
9 terms = 0.8414710097
it says to approximate with in 10^-4 which would be 0.8414. 7 terms looks good enough or by rounding do i need to go to 9 terms.
Should there be a formula to solve this or is it just manul computation?