vertrauensvoll
trusting
Full of trust; showing the attitude that one believes someone or something and relies on them.
Das Kind blickte seine Mutter vertrauensvoll an.
The child looked at his mother trustingly.

trusting / trustful
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trusting
Full of trust; showing the attitude that one believes someone or something and relies on them.
Das Kind blickte seine Mutter vertrauensvoll an.
The child looked at his mother trustingly.

The adjective is a compound made up of the noun 'das Vertrauen' (trust), the linking element '-s-', and the suffix '-voll' (full of). So it literally means 'full of trust'.
Sie hat ein sehr vertrauensvolles Verhältnis zu ihren Eltern.
She has a very trustful relationship with her parents.
The word describes either a person's attitude ('ein vertrauensvoller Blick' — a trusting look) or the quality of a relationship based on mutual trust ('eine vertrauensvolle Zusammenarbeit' — trustful cooperation).
Mit einer vertrauensvollen Geste legte er seine Hand auf ihre Schulter.
With a trusting gesture, he placed his hand on her shoulder.
Especially in professional life, people often speak of 'eine vertrauensvolle Zusammenarbeit' (trustful cooperation), 'eine vertrauensvolle Atmosphäre' (a trustful atmosphere), or 'ein vertrauensvolles Gespräch' (a trustful conversation).
Wir streben eine langfristige und vertrauensvolle Partnerschaft an.
We are aiming for a long-term and trustful partnership.
'Vertrauensvoll' can also be used as an adverb to describe how an action is carried out. A typical phrase is 'sich vertrauensvoll an jemanden wenden' (to turn to someone trustingly).
Sie wandte sich mit ihrem Problem vertrauensvoll an ihre beste Freundin.
She turned trustingly to her best friend with her problem.
skeptical
'skeptisch' and 'vertrauensvoll' describe opposite attitudes. Someone who is 'skeptisch' has doubts and examines a situation or a statement critically. Someone who is 'vertrauensvoll' is more likely to believe someone and rely on them. 'skeptisch' fits when you remain cautious and do not believe something right away. 'vertrauensvoll' fits when trust is central and you feel secure.

Der Patient sprach vertrauensvoll mit der Ärztin über seine Sorgen.
The patient spoke trustingly with the doctor about his worries.
Sie ist skeptisch, weil der Vertrag viele unklare Punkte enthält.
She is skeptical because the contract contains many unclear points.