Hyperbolic Sine Function The hyperbolic sine function is a function f: R → R is defined by f(x) = [e^{x}– e^{–}^{x}]/2 and it is denoted by sinh x. Sinh x = [e^{x}– e^{–}^{x}]/2. Graph : y = Sinh x.

Example: Graphing a Hyperbola Centered at (0, 0) Given an Equation in Standard Form. Graph the hyperbola given by the equation y264−x236=1 y 2 64 − x 2 36 = 1 . Identify and label the vertices, co-vertices, foci, and asymptotes. Plot and label the vertices and co-vertices, and then sketch the central rectangle.

Sinh is the hyperbolic sine function, which is the hyperbolic analogue of the Sin circular function used throughout trigonometry. It is defined for real numbers by letting be twice the area between the axis and a ray through the origin intersecting the unit hyperbola .

Hyperbolic functions are analogous to trigonometric functions but are derived from a hyperbola as trigonometric functions are derived from a unit circle. Hyperbolic functions are expressed in terms of the exponential function e^{x}. There are six hyperbolic functions are sinh x, cosh x, tanh x, coth x, sech x, csch x.

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