Domain and Range of Trigonometric Functions
For trigonometric functions, the domain is a set of all real numbers (except some values in some functions) and the range of the trigonometric functions varies with different trigonometric functions, such that
- Range of Sine Function = [-1, 1]
- Range of Cosine Function = [-1, 1]
- Range of Cosecant Function = (−∞,−1]∪[1,+∞)
- Range of Secant Function = (−∞,−1]∪[1,+∞)
The range for Tangent and Cotangent functions is different,
- Range of Tangent Function = [-∞, ∞]
- Range of Cotangent Function = [-∞, ∞]
This can be summarized in the table below:
Trigonometric Functions | Domain | Range |
---|---|---|
sin θ | R | [-1, 1] |
cos θ | R | [-1, 1] |
tan θ | R – (2n + 1)π/2 | R |
sec θ | R – (2n + 1)π/2 | (−∞,−1]∪[1,+∞) |
cosec θ | R – nπ | (−∞,−1]∪[1,+∞) |
cot θ | R – nπ | R |
Domain and Range of a Function
Domain and Range of a Function: Domain and Range are the input and output values of a Function. A function is defined as the relation between a set of inputs and their outputs, where the input can have only one output i.e. a domain can yield a particular range. It depicts a relationship between an independent variable and a dependent variable.
A function is usually denoted by y = f(x), where x is the input. A function is a relation f from a set X to another set Y, where each element in X has exactly one output in Y, and it is represented as f: X→Y. Here the set X is known as the domain of a function, and the set Y is called the co-domain of the function. Every function has a domain, codomain, and range that help in defining the function.
In this article, we will learn about the domain and range of a function, how to calculate the domain and range of a function, the domain and range of a function worksheet, the domain and range of a function examples, domain and range of a function graph, and others in detail.
Table of Content
- What is Domain and Range?
- Interval Notation of Domain and Range
- Co-Domain and Range
- Domain of a Function
- How to Find the Domain of a Function?
- Range of a Function
- How to Find the Range of a Function?
- How to Find Domain and Range
- Domain and Range of a Function Examples
- Quadratic Domain and Range
- Domain and Range of Exponential Functions
- Domain and Range of Trigonometric Functions
- Domain and Range of Inverse Trigonometric Functions
- Domain and Range of an Absolute Value Function
- Domain and Range of a Square Root Function
- Domain and Range of a Rational Function
- Log Function Domain and Range
- Domain and Range of Greatest Integer Function
- Domain and Range of a Function Graph
- Domain and Range of a Function Worksheet
- Domain and Range Worksheet PDF
- Domain and Range Practice Problems
- Solved Questions on Domain and Range