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- asinh()
### asinh()

# asinh()

asinh(expr0) ⇒ number

The asinh() function returns the inverse hyperbolic sine of the argument as a number. The corresponding mathematical notation and a mathematical identity of the function are:

asinh(x)

The domain is the whole real line.

Use the calculator at the top right of the window to find the inverse hyperbolic sine of a number. Click the [2

^{nd}] key at the top left of the keypad, then click [asinh].## Scientific calculator

## Note

**Why is it arsinh rather than arcsinh?**Ever wondered why we say

**arcsin**for the inverse of the sine function, but**arsinh**for the inverse of the hyperbolic sine function? It's because arcsin gives the**arc**length on the unit circle for a given*y*-coordinate, whereas arsinh gives an**area**enclosed by a hyperbola and two rays from the origin for a given*y*-coordinate. The red shaded area below is equal to arsinh(*a*), where*a*is the length of the blue line segment.Source : Text and figure by Patrick MacMahon, reproduced in full from Geogebra ↗.

## References