# Domain and range of trigonometric functions and their graphs

Function’s domain is defined as the particular set values that an independent variable contained in a function can accept the work. The range exists as resulting values which a dependent variable can hold a value of ‘x’ changes all through the domain.

## For Cosine and Sine Functions, the Range and Domain

There are no limitations on cosine and sine’s domain functions. So, their domain results in the form of x ∈ R.

It’s important to note that, nonetheless, the range for y = cos (x) and y = sin (x) is between the range of (-1 & 1). Hence, the changes found in these functions regarding stretches and shifts will result in affecting the range of trigonometric functions but not the domain of the trigonometric functions.

## Domain and Range of Sine Function

y = f(x)= Sin(x)

Range: The value lies between -1 ≤ y ≤ 1

Domain: It’s determined for all the ‘x’ real values

Period: 2π = 360º

Sine Function is an odd function

The Graph of sin(x) function:  ## Domain and Range of Cosine Function

y= f(x) = cos(x)

Range: the value lies between -1 ≤ y ≤ 1

Domain: Defined for all the x real values

Period: 2π

Cosine is an even function

The Graph of cos(x) function:

###   From the above graph, we can see that the range remains there and graph reduces

## Domain and Range for Tangent functions

Note that the function y = tan (x) consist of vertical asymptotes at . Hence,

For – y=f(x)=tan(x)

Range: All real numbers (or y ∈ R)

Tangent’s Domain: Defined for all x real values, except x ≠(2n + 1)(π/2), where n is any integer.

Period: π

Tangent is an odd function

As a result. from the above domain and range, changes will affect range but will affect the domain.

The Graph of tan(x) function ## Domain and Range For Cotangent Function

y=f(x)=cot(x)

Range: All the real numbers

Domain: Defined for all the x real values; except x ≠nπ, where n is any value of an integer

Period: π

Cotangent is an odd function

The Graph of cot(x) function ## Domain and Range For Secant Function

y=f(x)=sec(x)

Range : (-∞,-1] ∪ [1,∞)

Domain: It is defined for all real values of x except x ≠(2n + 1)(π/2) where n is any value of the integer

Period: 2π

Secant is an even function

The Graph of sec(x) function ## Domain and Range For Cosecant Function

y=f(x)=cosec(x)

Range: (-∞,-1] ∪ [1,∞)

Domain: Defined for all x real values; except x ≠nπ, where n exist as any integer value

Period: 2π

Cosecant is an odd function

The Graph of cosec(x) function ## Summary of all trigonometric functions and their graphs: Posted in A2