eagerly is the way of what is or is anxious. Waiting anxiously means that the individual is restless waiting for what will happen, and it can represent both a feeling of anguish and a feeling of great desire.
The word anxiously is an adverb so that it gives intensity to the adjective anxious or gives form to the noun anxiety. It accompanies the verb giving an idea of how the action is being carried out.
Anxiously is a circumstance of nervousness, restlessness, distress. It is the exaggerated desire for something to be completed, it is an exaggerated anxiety of tension and worry about some fact that is taking place.
For example:
The mother-to-be waits "anxiously" for the birth of the twins.
The boy is "eagerly" looking for a new job.
The speaker "anxiously" waits for the time to present their research.
The student "eagerly" participates in training for their new job.
The family "eagerly" lived life outside their country.
They are synonyms of eagerly: eagerly, impatiently, restlessly, restlessly and restlessly.
In English, eagerly is anxiously.
In Spanish, eagerly is the same: eagerly.
Eagerly or Eagerly
The correct spelling is eagerly. The word comes from the Latin anxiosus, which means restless. From Latin to modern Portuguese, the letter X undergoes an orthographic evolution to the letter S. Hence anxious, anxiety, anxious and their derivatives are spelled correctly with S, and never with C.