
hoffnungsvoll
hopeful
Describes a person who looks to the future full of hope and confidence.
Trotz der Niederlage blieb der Trainer hoffnungsvoll für das nächste Spiel.
Despite the defeat, the coach remained hopeful about the next game.
hopeful
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hopeful
Describes a person who looks to the future full of hope and confidence.
Trotz der Niederlage blieb der Trainer hoffnungsvoll für das nächste Spiel.
Despite the defeat, the coach remained hopeful about the next game.

promising
Describes a situation, a piece of news, or a development that gives reason for hope.
Die ersten Testergebnisse des neuen Medikaments sind sehr hoffnungsvoll.
The first test results for the new medication are very promising.
The adjective is made up of the noun 'die Hoffnung' (hope), the linking -s, and the word 'voll' (full). So it literally means “full of hope.”
Sie war hoffnungsvoll, dass alles gut werden würde.
She was hopeful that everything would turn out well.
'Hoffnungsvoll' (hopeful) can be used as an adjective before a noun, as part of the predicate with 'sein' (to be), or as an adverb to describe a verb.
Er warf ihr einen hoffnungsvollen Blick zu.
He gave her a hopeful look.
The word describes either a person's feeling or the potential of something. When it refers to a person, it means 'zuversichtlich' (confident/hopeful). When it describes a thing, such as a result or a talent, it means 'vielversprechend' (promising).
Der junge Pianist gilt als sehr hoffnungsvolles Talent.
The young pianist is considered a very promising talent.
optimistic
Optimistisch and hoffnungsvoll both describe a positive outlook on the future. Optimistisch more often means that someone expects a good outcome, while hoffnungsvoll also fits when there is mainly a wish or a reason for hope. Optimistisch is a good fit for a well-founded expectation; hoffnungsvoll is more suitable for cautious hope.

Nach den ersten Fortschritten ist der Trainer hoffnungsvoll, obwohl ein Sieg noch nicht sicher ist.
After the initial progress, the coach is hopeful, although a victory is not yet certain.
Nach den guten Nachrichten ist der Trainer optimistisch und rechnet mit einem Sieg.
After the good news, the coach is optimistic and expects a victory.