Hyperbolic Functions Calculator (sinh cosh tanh)

Enter x to compute sinh, cosh and tanh along with csch, sech and coth at once. Includes a graph and a check of the identity cosh squared minus sinh squared equals 1.

Input

Enter a real number x to compute the hyperbolic functions sinh, cosh and tanh and the reciprocals csch, sech and coth.

Value of x

Enter any real number

Result

sinh x

1.17520119

cosh x

1.54308063

tanh x

0.76159416

csch x

0.85091813

sech x

0.64805427

coth x

1.31303529

cosh squared minus sinh squared

For every real x, cosh x squared minus sinh x squared equals 1. The value above confirms this by being equal to 1.

How it works

sinh x equals e to the x minus e to the minus x divided by 2, cosh x equals e to the x plus e to the minus x divided by 2, and tanh x equals sinh x divided by cosh x.
csch x, sech x and coth x are the reciprocals of sinh x, cosh x and tanh x. Because sinh 0 equals 0, csch and coth are undefined when x is 0.
For every real number x the identity cosh x squared minus sinh x squared equals 1 holds. This tool displays the measured value so you can confirm it.
Values are shown with up to 8 decimal places to limit rounding error. The graph plots x over the range minus 3 to 3.

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