physicscatalyst.com logo




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




Related Topics


link to this page by copying the following text


Class 11 Maths Class 11 Physics





Note to our visitors :-

Thanks for visiting our website.
DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY DISCLOSURE FOR MORE INFO.