Thread: number of terms for approximation

given that sin(1) = 1 - 1/3! + 1/5! ... 1/(2i+1)! determin how many terms are needed to approximate sin(1) within 10^-4

Originally Posted by diroga

given that sin(1) = 1 - 1/3! + 1/5! ... 1/(2i+1)! determin how many terms are needed to approximate sin(1) within 10^-4

5! = 120
7! = 5040
1/5040 = 0.0001984

Therefore you need the next term:

1/9! = 0.000002755
That gives an approximate for the value required.

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?