Question

Reflecting the graph of y=cosx across the y axis is the same as not reflecting it at all.

True or False

Answer 1

Refrecting the graph of y = cos x across the y axis is the same as not refrecting it at all since y = cos x is an even function. i.e. cos x = cos (-x). Hence the statement is true.

Answer 2

True

Explanation:

The graph of
`y=\cos(x)` is an even function.

This means that the graph of
`y=\cos(x)` is symmetric about the y-axis.

If we reflect the graph of
`y=\cos(x)` about the y-axis, it will fall exactly on its outline.

This makes it behave as if it has not been reflected at all.

In other words, the mapping for reflection about the y-axis is

`(x,y)\rightarrow(-x,y)`

Since
`\cos(-x)=\cos(x)`

The graph will retrace its outline.