Question

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

Answer 1

Hence the function only :

Secx and Cosx functions are symmetric about y-axis

And remaining functions are not symmetric about y-axis.

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