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Hyperbolic Functions

★★★☆☆High School

📖Definition

Functions related to hyperbolas, similar in form to trigonometric functions but defined using exponentials.

sinh x = \frace^x - e^-x2

Hyperbolic sine

cosh x = \frace^x + e^-x2

Hyperbolic cosine

tanh x = (sinh x)/(cosh x) = \frace^x - e^-xe^x + e^-x

Hyperbolic tangent

cosh² x - sinh² x = 1

Hyperbolic identity (note sign difference from trig)

예제 1★★☆☆☆

Find sinh(0) and cosh(0).

예제 2★★★☆☆

Prove that cosh²(x) - sinh²(x) = 1.

Catenary curves, special relativity

Electric circuits, signal processing

tanh activation function

#쌍곡선함수#sinh#cosh#tanh#hyperbolic