Translation of "Broadly" in Japanese

He grinned broadly at us.

我々を見てにたりと笑った。

Well, broadly speaking that's right.

まあ、広義的には間違っていませんね。

Broadly speaking, dogs are more faithful than cats.

大まかに言って、犬は猫より忠実だ。

But I also think we can consider this concept much more broadly.

さらに私は このコンセプトを もっと広げて検討できると考えています