About Hyperbolic Functions Formula
Hyperbolic functions are exponential functions with features that are similar to trigonometric functions. These functions are similar to trigonometric functions in that they have the letter 'h' attached to their name. These are related to the hyperbola in the same way as trigonometric functions are related to the circle. As a result, they are referred to as hyperbolic functions collectively and as hyperbolic sine, hyperbolic cosine, and so on. They can be used as solutions to some partial differential equations in addition to modelling.
Hyperbola Equation (General) / Hyperbola Equation (Standard)
A hyperbola is a plane curve created by a point traveling so fast that the distance between two fixed points remains constant. The foci are the two fixed points, and the centre of the hyperbola is the mid-point of the line segment connecting the foci. The line that runs through the foci is known as the transverse axis. The conjugate axis is perpendicular to the transverse axis and passes through the centre.
The spots where the hyperbola contacts the transverse axis are known as the vertices. The distance between two foci is 2c. There is a 2a distance between the two vertices. The length of the transverse axis is also 2a s. The conjugate axis is 2b in length. b has the value.
Eccentricity of Hyperbola
- A hyperbola is a set of points in a plane where the difference between their distances from two fixed points is constant.
- In other words, the distance from a fixed point in a plane is proportionally bigger than the distance from a fixed point in a plane.
| The eccentricity of a Hyperbola: | For a Hyperbola, the value of eccentricity is: −[√(c2−a2)]/a |
| The Hyperbolic sine of x | Sinh x :(ex − e-x)/2 |
| The Hyperbolic cosine of x | Cosh x : (ex + e-x)/2 |
| The Hyperbolic tangent of x | Tanh x: sinh x/ cosh x = (ex - e-x)/ (ex + e-x) |
| The Hyperbolic cotangent of x | Coth x: cosh x/ sinh x = (ex + e-x) / (ex - e-x), where x is not equal to 0. |
| The Hyperbolic secant of x | Sech x: 1/ cosh x = 2/ (ex + e-x) |
| The Hyperbolic cosecant of x | Csch x: 1/ sinh x = 2/ (ex - e-x), where x is not equal to 0. |
- As a result, the Hyperbola's eccentricity is always bigger than 1, i.e. e > 1.
- The general hyperbola equation, often known as the standard hyperbola equation, is written as
- The lengths of the semi-major and semi-minor axes are the values a and b for each Hyperbola.
Maths Formulas prepared by HT experts are listed on the main page.
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