What is the importance of $\sinh(x)$? I stumbled across $\sinh(x)$. I am only a calculus uno student, but was wondering when this function comes into play, and what is its purpose? Last, does it have world applications, or is it a human-made concept?

The hyperbolic sine (and the hyperbolic cosine) arises naturally in the solution to the differential equation
$$f''=f$$
which is
$$f(x)=a\sinh(x)+b\cosh(x)$$
