Arccos 5 13

Arccos 5 13

Input
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

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