IPA: /ˌtrɛpɪˈdeɪʃəsli/
KK: /trɛpɪˈdeɪʃəsli/
In a way that shows fear or anxiety about something that may happen.
She approached the dark room trepidatiously, unsure of what she would find inside.
Trepidatiously → It is formed from "trepidare" (meaning to tremble) and the suffix "-ious" (meaning characterized by). The word describes a manner characterized by trembling or fear, often associated with anxiety or apprehension.
Think of someone who is 'trembling' ('trepidare') due to fear or anxiety — that's why acting trepidatiously means doing so in a fearful or anxious manner.