Statement: An even function rotated about the origin, where is any integer, remains an even function.

The statement is true.

Reflecting a graph across the -axis and then across -axis is equivalent to rotating the graph of around the origin.

For even values of , the function will be rotated multiples of , thus returning the function to its starting position.

For odd value of , the function will be rotated multiples of about the origin.

This results in a reflection in the -axis. Reflections in the -axis result in -values switching signs, which allows the function to remain even.

The statement is true.