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:**

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## 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**