AS/A2 Pure 4 Pure 5

P6 Topic 4: Maclaurin and Taylor series
The power series for sin(x)
The display shows the graph of y = sin x. Also shown is the graph of the curve :
By using the slider you can vary the value of n from 0 to 20

This display shows the same information numerically. Keep x as 1, and hence find what value of n gives sin 1 correct to 8 decimal places.

Summary Clearly, as n becomes bigger, the curve of the equation: becomes closer to the curve of y = sin x. Convergence is quite fast. You will need to make n=3 and x=1 to get an approximation to sin 1 that is correct to 3 decimal places. For 8 decimal place accuracy you will need to make n=5 and x=1. Based on free Java applets from JavaMath