## Taylor series for sinx centered at pi

Input interpretation |
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series | sin(x) | point | x = pi |

Series expansion at x=π |

-(x – pi) + 1/6 (x – pi)^3 – 1/120 (x – pi)^5 + O((x – pi)^7) (Taylor series) (converges everywhere) |

Approximations about x=π up to order 3 |

(order n approximation shown with n dots) |

Series representation at x=π |

sum_(n>=0)-(i i^n (-1 + (-1)^n) (-pi + x)^n)/(2 n!) |