A registered dental hygienist is authorized to perform the following procedures under direct supervision of a licensed dentist, after submitting to the dental hygiene board evidence of satisfactory completion of a course of instruction, approved by the dental hygiene board, in the procedures:
(a) Soft-tissue curettage.
(b) Administration of local anesthesia.
(c) Administration of nitrous oxide and oxygen, whether administered alone or in combination with each other.