Question

Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis. Is this statement true or false?

Answer 1

This statement is true.

Answer 2

The statement is true.

Explanation:

Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.

To find : Is this statement true or false?

Solution:

Rules of reflection :

Along across y-axis if we have a point
`(x,y)\rightarrow(-x,y)`

So, y=sinx

The reflection across y-axis→
`y=sin(-x) \Rightarrow y = -sinx`.......[1]

Along across x-axis if we have a point
`(x,y)\rightarrow(x,-y)`

so, y=sinx

The reflection across x-axis →
`-y=sinx\Rightarrow y= -sinx` .....[2]

Hence, [1] and [2] both of them are equal

Therefore, the statement is true.