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Sine

the sine function.


Series definitionEdit

$ \begin{align} \sin x & =\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}x^{2n+1} \\[8pt] & = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \frac{x^{11}}{11!} + \cdots \\[8pt] \end{align} $
3rd-degree-taylorsine

The sine function being approximated by it's 3rd degree taylor Polynomial.for almost half a cycle.

5th-degree-taylorsine

The sine function being approximated by it's 5th degree taylor Polynomial.

7th-degree-taylorsine

The sine function being approximated by it's 7th degree taylor Polynomial.for almost a full cycle.

9th-degree-taylorsine

The sine function being approximated by it's 9th degree taylor Polynomial.

11th-degree-taylorsine

The sine function being approximated by it's 11th degree taylor Polynomial.

Contenuid FractionEdit

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