Bowing for alenu and other places

Can one bow in any direction for alenu and other places matter? Does it have to be “east?”

I include in this “other places” the bowing in the amida, since I’ve been in bate keneset where the hehal is not “east,” and everyone is facing some other direction.

Thank you.

The amida should be said facing east.

Bowing should be done facing east as well.