cos(200!)

In a footnote to the previous post, I said that Python’s math library can calculate the logarithm of extremely large numbers but not the cosine. This post will expand on that comment. In this post I’ll use n = 200! as my example rather than 1000! nbecause this value of N is larger than the largest representable floating point number but small enough to be more convenient to work with. Suppose someone calculates 200! for you: 78865786736479050355236321393218506229513597768717326329474253324435\ 94499634033429203042840119846239041772121389196388302576427902426371\ 05061926624952829931113462857270763317237396988943922445621451664240\ 25403329186413122742829485327752424240757390324032125740557956866022\ 60319041703240623517008587961789222227896237038973747200000000000000\ 00000000000000000000000000000000000 You could now calculate log(n) using n = 7.886578673647905 × 10374 and so log(n) = log(7.886578673647905 × 10374) = log(7.886578673647905) + 374 log(10) = 863.2319871924055. The key…