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sin(0.02) - 0.02  =   -0.00000133330666692 … [1]
How many terms of Maclaurin series do I need
to calculate sin(x)-x at x=0.02 with the same result?
First term:
sin(0) - 0  =   0.0 [2]
Plus second term:
ans + (cos(0) - 1) * 0.02  =   0.0 [3]
Plus third term:
ans + ( - sin(0)) / 2 * 0.02**2  =   0.0 [4]
Plus fourth term:
ans - cos(0) / fact(3) * 0.02**3  =   -0.00000133333333333 … [5]
Odd terms have sin(0) therefore they can be skipped.
Plus sixth term:
ans + cos(0) / fact(5) * 0.02**5  =   -0.00000133330666667 … [6]
Plus eighth term:
ans - cos(0) / fact(7) * 0.02**7  =   -0.00000133330666692 … [7]
Eight terms! So with eight terms, what is the error?
[1] - [7]  =   1.41092961361E-21 … [8]
Of course much of this error is the 10th term:
cos(0) / fact(9) * 0.02**9  =   1.41093474427E-21 … [9]
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