Home page for accesible maths Math 101 Chapter 4: Taylor series and complex numbers 4.8 The Maclaurin series for sine 4.10 The general binomial theorem

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4.9 Numerical values

\sin x=x-{{x^{3}}\over{3!}}+{{x^{5}}\over{5!}}-\dots.

Let $p_{3}(x)=x-x^{3}/6$ . The quality of the approximation can be judged from the following table. Here the percentage relative error is $R=100|p_{3}(x)-\sin x|/\sin x$ .

x\qquad\qquad\sin x\qquad p_{3}(x)\qquad\quad R

0.01\qquad\quad 0.0099998\quad 0.0099998\quad 0

0.10\qquad\quad 0.0998334\quad 0.0998333\quad 10^{-4}

1.00\qquad\quad 0.8414709\quad 0.8333333\quad 1

2.00\qquad\quad 0.9092974\quad 0.6666667\quad 27