This is the 3556th most frequent Portuguese word.
profunda
Deep.
Here, 'profunda' is an adjective describing the depth of the analysis, metaphorically referring to its thoroughness and detail.
A análise do texto foi muito profunda.
The analysis of the text was very deep.
In this case, 'profunda' (used as 'profundo') modifies 'suspiro' to express the physical or emotional depth of the sigh.
Ela deu um suspiro profundo antes de começar a falar.
She took a deep sigh before starting to speak.
The word 'profundos' describes the nature of the feelings, figuratively indicating their complexity and intensity.