Ever wondered why we say [b]arcsin[/b] for the inverse of the sine function, but [b]arsinh[/b] for the inverse of the hyperbolic sine function? It's because arcsin gives the [b]arc[/b] length on the unit circle for a given [i]y[/i]-coordinate, whereas arsinh gives an [b]area[/b] enclosed by a hyperbola and two rays from the origin for a given [i]y[/i]-coordinate. The red shaded area below is equal to arsinh([i]a[/i]), where [i]a[/i] is the length of the blue line segment.