Question

The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:

Answer 1

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:

                    $f(-x)=-f(x)$

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:

                      $f(-x)=f(x)$

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,

$\tan(-x)=-\tan x\\\\\cos (-x)=-\cot x\\\\\csc (-x)=-\csc x$

( 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.