Respuesta :
Answer:
The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:
Origin.
Step-by-step explanation:
A function f(x) is said to be a odd function if:
[tex]f(-x)=-f(x)[/tex]
Also, an odd function always has a symmetry with respect to the origin.
whereas a function f(x) is said to be a even function if:
[tex]f(-x)=f(x)[/tex]
Also, an even function has a symmetry with respect to the y-axis.
We know that:
Tangent function, cotangent function and cosecant function are odd functions.
Since,
[tex]\tan(-x)=-\tan x\\\\\cos (-x)=-\cot x\\\\\csc (-x)=-\csc x[/tex]
( similarly sine function is also an odd function.
whereas cosine and secant function are even functions )
Hence, the graph of tangent function, cotangent function and cosecant function is symmetric about the origin.
