# Arccos 5 13

Input |
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cos^(-1)(5)×13 |

Exact Result |

13 cos^(-1)(5) (result in radians) |

Decimal approximation |

29.80161170429530994141023504752420061108428712020423321886… i (result in radians) |

Polar coordinates |

r~~29.8016 (radius), theta~~90° (angle) |

Continued fraction |

[30i; 5i, -25i, -3i, -3i, -3i, -4i, 6i, -26i, -11i, 2i, -3i, -16i, -2i, 4i, 2i, -, …] (using the Hurwitz expansion) |

Integral representation |

cos^(-1)(5) 13 = 13 integral_5^1 1/sqrt(1 – t^2) dt |

Continued fraction representation |

cos^(-1)(5) 13 = 13/2 (pi – (20 i sqrt(6))/(1 + K_(k=1)^infinity (-50 floor((1 + k)/2) (-1 + 2 floor((1 + k)/2)))/(1 + 2 k))) = 13/2 (pi – (20 i sqrt(6))/(1 + -50/(3 – 50/(5 – 300/(7 – 300/(9 + …)))))) for 5>=infinity |