Tan 90 degrees: Overview, Questions, Preparation

Hyperbolic functions are similar in mathematics to trigonometric functions or spherical functions. Hyperbolic functions are typically defined by algebraic expressions, including the exponential function (ex) and its inverse exponential functions (e-x), where e is the constant of Euler. 

The hyperbolic functions are analogs of the trigonometric function or the spherical function. In the solutions of linear differential equations, an approximation of distance and angles in hyperbolic geometry, Laplace's equations in cartesian coordinates, and the hyperbolic function occur. Generally, in the true statement called the hyperbolic angle, the hyperbolic function takes place. The hyperbolic fundamental functions are:

1. Sine Hyperbolic (sinh)
2. Cosine Hyperbolic (cosh)
3. Tangent Hyperbolic (tanh)

The other functions such as hyperbolic cosecant (cosech), hyperbolic secant(sech), and hyperbolic cotangent (coth) functions are derived from these three basic functions. Let us address in detail the simple hyperbolic functions, diagrams, properties, and hyperbolic inverse functions.

1. Sinhx = ex -e-x/2
2. Coshx = ex + e-x/2
3. Tanhx = ex-e-x/ex +e-x

Properties of Hyperbolic Functions

The properties of hyperbolic functions are analogous to the trigonometric functions. Some of them are:

1. Sinh (-x) = -sinh x
2. Cosh (-x) = cosh x
3. Sinh 2x = 2 sinh x cosh x
4. Cosh 2x = cosh 2x + sinh 2x

The derivatives of hyperbolic functions are:

1. d/dx sinh (x) = cosh x
2. d/dx cosh (x) = sinh x

Some relations of hyperbolic function to the trigonometric function are as follows:

1. Sinh x = – i sin (ix)
2. Cosh x = cos (ix)
3. Tanh x = – i tan (ix)

Hyperbolic Functions in Class 11:

In trigonometry, there is a small introduction of hyperbolic function you will get to learn about all the basics of hyperbolic function in it. The weightage of trigonometry in Class 11 is 23 marks.

Hyperbolic Functions in Class 12:

There are some problems in calculus where you will need to have some knowledge about the basics and properties of the hyperbolic function. The weightage of Calculus is 22 marks in the board exam.

1. What is cosech?

The Hyperbolic Cosecant Function. cosech(x) = 1 / sinh(x) = 2 / (ex − e−x) 

2. What's the distinction between trigonometric and hyperbolic functions?

Hyperbolic functions in mathematics are analogs of ordinary trigonometric functions, except they are defined by the hyperbola rather than the circle. Much as a circle with a unit radius is formed by the points (cos t, sin t), the points (cosh t, sinh t) form the right half of the unit hyperbola.

3. What is Sinh equal to?

sinh(x) = ex − e−x 2.

Q: What do hyperbolic functions mean?

Q: What are Coshx and Sinhx?

Q: What are Coshx and Sinhx?

Q: What is a hyperbolic example?

Q: Are periodic hyperbolic functions?

Q: Is the opposite Sinh sine?