A hyperbolic function is a type of mathematical function that is defined using the hyperbolic sine (sinh) and hyperbolic cosine (cosh) functions. These functions are similar to the regular sine and cosine functions, but they use the exponential function instead of the circular function.
The graph of a hyperbolic function has a different shape compared to a regular trigonometric function. While the graph of a regular trigonometric function is a periodic wave, the graph of a hyperbolic function is a symmetrical curve that approaches two parallel lines called asymptotes.
The most common hyperbolic functions are the hyperbolic sine (sinh), hyperbolic cosine (cosh), hyperbolic tangent (tanh), hyperbolic cotangent (coth), hyperbolic secant (sech), and hyperbolic cosecant (csch). These functions are used in various mathematical and scientific applications.
To graph a hyperbolic function, you can plot points on a coordinate plane using a table of values or use a graphing calculator. The key points to plot are the x-intercepts, y-intercepts, and points where the function crosses the asymptotes. From these points, you can sketch the curve of the hyperbolic function.
Hyperbolic functions have many real-world applications, including physics, engineering, and economics. They are used to describe the shape of hanging cables and arches, the motion of a spring, and the growth of bacteria. They also have applications in signal processing, electrical engineering, and financial modeling.