# What are Transcendental Functions?

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## Transcendental Functions

Outline

• Introduction
• Examples
• Graphical Behavior of Sin (r)
• Graphical Behavior of cos (r)
• Graphical Behavior of tan (r)
• Graphical Behavior of e-x
• The graphical representation of ex
• The graphical representation of e power -x square (e^ (-x^2))
• The graphical representation of e power x square (e^(x^2))
• FAQs
• References

Introduction:

The definition of transcendence is to go past a limit or a boundary. A function in mathematics that cannot be expressed by combining addition, subtraction, multiplication, division, raising to a power, and taking the root. The functions log, sin, cos, and ex, as well as any functions containing them, are examples. The exponential function, trigonometric functions, and their inverses are all examples of transcendental functions. First, according to Euler, some operations are transcendental. He referred to the following operations as algebraic even though they took place in a section discussing functions: addition, subtraction, multiplication, division, raising to a power, and the extraction of root. The algebraic functions are those which can be written in the form of algebraic expression. The transcendental functions are those which are not algebraic. Some functions are algebraic, but some are transcendental.

Examples of Transcendental functions:

There are three types of transcendental functions like,

Trigonometric Functions:

There are 3 basic trigonometric functions, sin(r), and cos(r), tan(r). The other three trigonometric functions like, sec (r), cosec(r) and cot (r) are made by three basic trigonometric functions. In this section we will discuss the graphs of sin(r), and cos(r), tan(r) in 3-dimension.

Graphical Behavior of Sin (r):

The graphical representation of transcendental function sin (r) in 3-dimensional is shown in figure no.1 and figure no.2.

• The sin curve is sinusoidal.
• The behavior of sin curve is decreasing and increasing.

Graphical Behavior of cos (r):

The graphical representation of transcendental function cos (r) in 3-dimensional is shown in figure no.3 and figure no.4.

• The cos curve is initially increase then decrease and with the passage of time it again increases.
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Graphical Behavior of tan (r):

The graphical representation of transcendental function tan (r) in 3-dimensional is shown in figure no.5 and figure no.6.

The tan function is a ratio of cos and sin function i.e.

Tan (r) = sin(r) / cos(r)

So, the curve of tan is the combination of curve of sin as well as cos.

• The tan curve is initially constant then increase at the same point it is increase.
• Then it again become constant then increase at the same point it decrease and at the end it again become constant.

Exponential functions:

Exponential functions are transcendental functions like, e-x,ex etc.

In this section we will discuss the graphical behavior of exponential functions in 3-dimensuinal.

Graphical Behavior of e-x:

The graphical representation of e-xis shown in figure no.7.

The graphical representation of ex

The graphical representation of ex is shown in figure no.8.

The graphical representation of e power -x square (e^(-x^2))

The graphical representation of e power -x square (e^(-x^2)) is shown in figure no.9.

The graphical representation of e power x square (e^(x^2)):

The graphical representation of e power x square (e^(x^2)) is shown in figure no.10.

FAQs:

1. What are transcendental functions?

A function in mathematics that cannot be expressed by combining addition, subtraction, multiplication, division, raising to a power, and taking the root.

2. How many types of transcendental functions?

there are three types of transcendental functions discussed below,

• Trigonometric Functions
• Exponential Functions
• Inverse of trigonometric functions and exponential functions.

3. What is the behavior of curve of transcendental function cos (r)?

The cos curve is initially increase then decrease and with the passage of time it again increases.

4. What is the behavior of curve of transcendental function tan (r)?

The tan function is a ratio of cos and sin function i.e.

Tan (r) = sin(r) / cos(r)

So, the curve of tan is the combination of curve of sin as well as cos.

• The tan curve is initially constant then increase at the same point it is increase.
• Then it again become constant then increase at the same point it decreases and at the end it again become constant.

5.What is the behavior of curve of transcendental function sin (r)?

• The sin curve is sinusoidal.
• The behavior of sin curve is decreasing and increasing.

References:

Larson, R. and Edwards, B.H., 2010. Calculus: Early transcendental functions. Cengage Learning.