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Domain ,Range and Graphs of Trigonometric functions





Sine Function

y=f(x)= Sin(x)
domain : It is defined for all real values of x
range : -1 ≤ y ≤ 1
Period:2π
It is a odd function
Graph of sin(x) function
graph of sin(x) function

More Graphs on sine function for y=f(x)=2 sin (x) and y=f(x)=3 sin (x)
graph of multiple of sin(x) function
We can see that range get increased in the similar way
for y=f(x)=sin (2x)
graph of sin(2x) function
We can see that range remains but graph get shrink

Cosine Function

y=f(x)= cos(x)
Domain : It is defined for all real values of x
Range : -1 ≤ y ≤ 1
Period:2π
It is even function
Graph of cos(x) function
graph of cos(x) function

More Graphs on contains function for y=f(x)=2 cos (x) and y=f(x)=3 cos (x)
graph of multiple of cos(x) function
We can see that range get increased in the similar way
for y=f(x)=cos (2x)
graph of cos(2x) function
We can see that range remains but graph get shrink



Tangent Function

y=f(x)=tan(x)
Domain : It is defined for all real values of x except x ≠(2n + 1)(π/2) where n is any
Range : All the real numbers
Period:π
It is a odd function
Graph of tan(x) function
graph of tan(x) function

Cotangent Function

y=f(x)=cot(x)
Domain : It is defined for all real values of x except x ≠nπ, where n is any integer
Range : All the real numbers
Period:π
It is a odd function
Graph of cot(x) function
graph of cot(x) function

Secant Function

y=f(x)=sec(x)
Domain : It is defined for all real values of x except x ≠(2n + 1)(π/2) where n is any integer
Range : (-∞,-1] ∪ [1,∞)
Period:2π
It is even function
Graph of sec(x) function
graph of sec(x) function

Cosecant Function

y=f(x)=cosec(x)
Domain :It is defined for all real values of x except x ≠nπ, where n is any integer
Range : (-∞,-1] ∪ [1,∞)
Period:2π
It is odd function
Graph of cosec(x) function
graph of cosec(x) function

We can write the range for the trigonometric functions in below summary table
Range of Trigonometric Functions



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