Can someone help me with understanding circular and hyperbol

Can someone help me with understanding circular and hyperbolic functions?

Solution

That is one vast field beyond the perview of a single questions. Still I would like to take you through the basics of these 2 type of functions -

Trigonometric functions are also called circular functions

The circle x² + y² = 1 can be parametrized by the functions x = cos(), y = sin().

Since these functions satisfy cos²() + sin²() = 1

Hyperbolic functions are a parametrization of a hyperbola

The hyperbolax² - y² = 1 can be parametrized by the functions x = f (u), y = g(u),

satisfying the condition f²(u) g²(u) = 1

The hyperbolic trigonometric functions are defined by

cosh(u) = 1/2 (e^u + e^u) , sinh(u) = 1/2 (e^u - e^u) .

cosh²(x) sinh²(x) = 1