Answer:
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:
<em>The function is said to be symmetric about the y-axis is given by</em>
<em>f(x)=f(-x)</em>
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
