Hyperbolic Functions Formulas
Various hyperbolic function formulas are,
sinh(x) = (ex – e-x)/2
Function | Definition |
---|---|
Hyperbolic Cosine (cosh x) | cosh(x) = (ex + e-x)/2 |
Hyperbolic Sine (sinh x) | |
Hyperbolic Tangent (tanh x) | tanh(x) = sinhx/coshx = (ex – e-x)/(ex + e-x) |
Hyperbolic Cotangent (coth x) | coth(x) = cosh x/sin hx = (ex + e-x)/(ex – e-x) |
Hyperbolic Secant (sech x) | ech(x) = 1/cosh x = 2/(ex + e-x) |
Hyperbolic Cosecant (csch x) | csch(x) = 1/sinh x = 2/(ex – e-x) |
Domain and Range of Hyperbolic Functions
Domain and Range are the input and output of a function, respectively. The domain and range of various hyperbolic functions are added in the table below:
Hyperbolic Function | Domain | Range |
---|---|---|
sinh x | (-∞, +∞) | (-∞, +∞) |
cosh x | (-∞, +∞) | [1, ∞) |
tanh x | (-∞, +∞) | (-1, 1) |
coth x | (-∞, 0) U (0, + ∞) | (-∞, -1) U (1, + ∞) |
sech x | (-∞, + ∞) | (0, 1] |
csch x | (-∞, 0) U (0, + ∞) | (-∞, 0) U (0, + ∞) |
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