{"content":"Hyperbolic versions of latest posts\n\nThe post A curious trig identity contained the theorem that for real x and y,\n\nThis theorem also holds when sine is replaced with hyperbolic sine.\n\nThe post Trig of inverse trig contained a table summarizing trig functions applied to inverse trig functions. You can make a very similar table for the hyperbolic counterparts.\n\nThe following Python code doesn’t prove that the entries in the table are correct, but it likely would catch typos.\n\n    from math import *\r\n\n    def compare(x, y):\r\n        print(abs(x - y) < 1e-12)\r\n\n    for x in [2, 3]:\r\n        compare(sinh(acosh(x)), sqrt(x**2 - 1))\r\n        compare(cosh(asinh(x)), sqrt(x**2 + 1))\r\n        compare(tanh(asinh(x)), x/sqrt(x**2 + 1))\r\n        compare(tanh(acosh(x)), sqrt(x**2 - 1)/x)                \r\n    for x in [0.1, -0.2]:\r\n        compare(sinh(atanh(x)), x/sqrt(1 - x**2))\r\n        compare(cosh(atanh(x)), 1/sqrt(1 - x**2)) \r\n\nRelated post: Rule for converting trig identities into hyperbolic identities\n\nThe post Hyperbolic versions of latest posts first appeared on John D. Cook.","contentType":"text/plain;utf-8","attachments":[],"quotePin":""}