How this calculator works
Cosh averages exponential growth and decay. Its graph is symmetric about zero and never falls below one. Both x and -x give the same height, which is why a reverse cosh calculation normally has two answers. The sign selector applies only to cosh and sech. Other inverse functions already determine the sign. The companion readouts use the recovered argument.
Formula
cosh x = (exp x + exp(-x))/2; sinh x = (exp x - exp(-x))/2; tanh x = sinh x/cosh x; sech x = 1/cosh x; cosh x = y gives x = ±acosh(y).
Worked example
At x = ln 2, cosh x = (2 + 0.5)/2 = 1.25 and sinh x = 0.75. Starting from cosh x = 1.25 recovers x = ±ln 2.
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Frequently asked questions
Is x measured in degrees?
No. This hyperbolic parameter is dimensionless; a degree conversion would change the intended calculation.
Can cosh be zero?
No real argument gives zero. Its minimum is one at x = 0.
Why are some companions undefined at zero?
Coth and csch divide by sinh x, which is zero there.