How this calculator works
Hyperbolic functions are combinations of exponentials rather than circular angle ratios. Reciprocals are evaluated from sinh, cosh or tanh. Their real inverse domains differ, so the selected function determines which inputs are allowed. The inverse sech uses the non-negative principal inverse, while inverse csch keeps the sign of its input.
Formula
sinh(x) = (exp(x)-exp(-x))/2; cosh(x) = (exp(x)+exp(-x))/2; tanh(x) = sinh(x)/cosh(x). csch, sech and coth are reciprocals.
Worked example
cosh(0) = (1 + 1)/2 = 1. Since sinh(ln 2) = (2 - 1/2)/2 = 3/4, asinh(0.75) = ln 2, approximately 0.69314718056.
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Frequently asked questions
Should x use degrees?
No. Hyperbolic functions take a dimensionless real parameter. Degree-to-radian conversion is not applied.
Why does acosh reject zero?
Real cosh is at least one, so zero has no real inverse cosh value.
What is the difference between asinh and csch?
asinh reverses sinh; csch is its reciprocal, 1/sinh(x).