Write all functions that are symmetric about the y-axis. Choose from the following six circular functions. yequals=sine xsinx , y equals=cosine xcosx , y equals=tangent xtanx , yequals=cotangent xcotx , y equals=secant xsecx , and yequals=cosecant x

Hence the function only:

Secx and Cosx functions are symmetric about y-axis

And remaining functions are not symmetric about y-axis.

Step-by-step explanation:

Given:

Six circular function as:

y = sinx, y=cosx, y=tanx, y = cotx, y=secx y=cosecx

To Find:

Which functions are symmetric about the y-axis

Solution:

The function is said to be symmetric about the y-axis is given by

f (x) = f (-x)

Now

1) For y=sinx i. e. f (x) = sinx

So put x=-x

f (-x) = sin (-x)

=-sinx

Hence f (x) ≠f (-x)

This function is not symmetric about y-axis

2) For y=cosx, i. e. f (x) = cosx

put x=-x

f (-x) = cos (-x) ... (as value for x and - x cos value remain the same)

=cosx

hence f (x) = f (-x)

This function is symmetric to the y-axis

3) For y=tanx i. e f (x) = tanx

put x=-x

f (-x) = tan (-x)

=-tanx

Hence f (x) ≠f (-x)

This function is not symmetric about y-axis

4) For y=cotx i. e. f (x) = cotx

Using above observation,

f (x) ≠f (-x)

This is not symmetric about y-axis

5) For y=secx i. e f (x) = secx

f (x) = f (-x)

This function is symmetric about y-axis.

6) for y=cosecx

f (x) ≠f (-x)

This function is not symmetric about y-axis