* 決意 (けつい - ketsui): This means "determination" or "resolve." It's a good choice if you're talking about a firm decision to do something. This is probably the closest single word equivalent.
* 意志 (いし - ishi): This means "will" or "intention." It emphasizes the mental aspect of being determined.
* 断固 (だんこ - danko): This means "firmly" or "resolutely." It highlights the unwavering aspect of determination.
* 固執 (こしゅう - koshu): This means "perseverance" or "obstinacy." It implies a strong adherence to one's goals, even if it borders on stubbornness.
Therefore, there's no single "correct" answer. The best kanji to use will depend on the context. If you can provide more context (e.g., a sentence where you want to use "determined"), I can give you a more precise suggestion.