The function sinh(x), or hyperbolic sine, is a mathematical function defined as the average of the exponential function. It is expressed as \sinh(x) = \frace^x - e^{-x}2 , where e is the base of natural logarithms. This function is useful in various fields, including engineering and physics, particularly in problems involving hyperbolic geometry. The graph of sinh(x) resembles that of the regular sine function but is unbounded and increases exponentially as x moves away from zero. At x = 0 , sinh(0) equals zero, and the function is odd, meaning sinh(-x) equals -sinh(x). This symmetry makes it a valuable tool in mathematical analysis.