Question

State the definition of the hyperbolic cosine and hyperbolic sine functions.

Short answer

Question: Provide the definitions of the hyperbolic cosine and hyperbolic sine functions. Answer: The hyperbolic cosine function (cosh(x)) is defined as cosh(x) = (e^x + e^{-x}) / 2, and the hyperbolic sine function (sinh(x)) is defined as sinh(x) = (e^x - e^{-x}) / 2, where "e" is the base of the natural logarithm (approximately 2.718) and "x" is the input value for the function.

Step-by-step solution

Definition of Hyperbolic Cosine (cosh) function

The hyperbolic cosine function, denoted by "cosh(x)", is defined in terms of exponential functions as follows: cosh(x) = \frac{e^x + e^{-x}}{2} Where "e" is the base of the natural logarithm (approximately equal to 2.718) and "x" is the input value for the function.

Definition of Hyperbolic Sine (sinh) function

The hyperbolic sine function, denoted by "sinh(x)", is defined in terms of exponential functions as follows: sinh(x) = \frac{e^x - e^{-x}}{2} Where "e" is the base of the natural logarithm (approximately equal to 2.718) and "x" is the input value for the function.