Properties of Hyperbolic Functions
Various properties of the hyperbolic functions are added below,
- sinh (-x) = – sinh(x)
- cosh (-x) = cosh (x)
- tanh (-x) = – tanh x
- coth (-x) = – coth x
- sech (-x) = sech x
- csc (-x) = – csch x
- cosh 2x = 1 + 2 sinh2(x) = 2 cosh2x – 1
- cosh 2x = cosh2x + sinh2x
- sinh 2x = 2 sinh x cosh x
Hyperbolic functions are also derived from trigonometric functions using complex arguments. Such that,
- sinh x = – i sin(ix)
- cosh x = cos(ix)
- tanh x = – i tan(ix)
- coth x = i cot(ix)
- sech x = sec(ix)
Hyperbolic Function
Hyperbolic Functions are similar to trigonometric functions but their graphs represent the rectangular hyperbola. These functions are defined using hyperbola instead of unit circles. Hyperbolic functions are expressed in terms of exponential functions ex.
In this article, we will learn about the hyperbolic function in detail, including its definition, formula, and graphs.
Table of Content
- What are Hyperbolic Functions?
- Hyperbolic Functions Formulas
- Domain and Range of Hyperbolic Functions
- Properties of Hyperbolic Functions
- Hyperbolic Trig Identities
- Inverse Hyperbolic Functions