What is the character used for the verb to sweat? 汗をかく
The kanji is 掻. Let me describe how you can check.
When you type the expression in with your IME, often a dictionary with appear with usage information. On my system, when I type かく, to the side a window with details on 掻く, 書く, 描く, and 搔く appears. For 掻く it says: （頭・あぐら・汗・いびき・裏・寝首・恥・べそを）⇒かく ＊掻く：常用外 ＊簡易慣用字体
Note arrow suggesting that it be written in hiragana. Also note the * which indicates that it is not included in basic kanji, and hence is not typically written in kanji.
Also, the dictionary is often useful. Quote:
Note the × before the headword. This indicates that it is not generally written in kanji. Same details as above.