It is well-known that Sita is a pativratā. But does she know that she is a pativratā? I mean does she declare anywhere in the Ramayana that she is?
Sita Devi is a Pativrata. She knows it better than any other. She declares it several times. That is how we know it too.
dīno vā rājyahīno vā yo me bhartā sa me guruḥ |
taṃ nityamanuraktāsmi yathā sūryaṃ suvarcalā || 5-24-9
"Although wretched or without kingdom, whoever is my husband, He alone is my master. Like Suvarchala with the Sun God, I am fond of Him always."
yathā śacī mahābhāgā śakraṃ samupatiṣṭhati |
arundhatī vasiṣṭhaṃ ca rohiṇī śaśinaṃ yathā || 5-24-10
lopāmudrā yathāgastyaṃ sukanyācyavanaṃ yathā |
sāvitrī satyavantaṃ ca kapilaṃ śrīmatī yathā || 5-24-11
saudāsaṃ madayantīva keśinī sagaraṃ yathā |
naiṣadhaṃ damayantīva bhaimī patimanuvratā || 5-24-12
tathāhamikṣvākuvaraṃ rāmaṃ patimanuvratā |
"Like the highly fortunate Sachi who waits upon Indra, like Arundhati on Vasishta, like Rohini on the Moon God, like Lopamudra on Agastya, like Sukanya on Chyavana, like Savitri on Satyavanta, like Srimati on Kapila, like Madayanti on Saudasa, like Kesini on Sagara, like Damayanti the daughter of Bhima, devoted to husband Nala, in the same way I am devoted to my husband Rama, the best in Ikshvaku dynasty."
This is the reply to Sita Devi to ogres in the Ashokavana.
Later when Ravana orders rakshasas to light up the tail of Hanuman, Sita devi again uses her chastity and prays to Agni to be friendly to Hanuman.
yadi asti pati śuśrūṣā yadi asti caritam tapaḥ || 5-53-28
yadi ca asti eka patnītvam śīto bhava hanūmataḥ |
yadi kaścit anukrośaḥ tasya mayi asti dhīmataḥ || 5-53-29
yadi vā bhāgya śeṣam me śīto bhava hanūmataḥ |
yadi mām vṛtta sampannām tat samāgama lālasām || 5-53-30
sa vijānāti dharma ātmā śīto bhava hanūmataḥ |
"If I have done any service to my husband, if I have performed a penance and if I am a faithful wife, please be cool to Hanuma."
"If the wise Rama has even a little of kindness to me and if I have still some good fortune remaining to my credit, please be cool to Hanuma."
"If that virtuous Rama recognises me as one,, who is endowed with a good moral conduct and who is ardently desirous of meeting him, please be cool to Hanuma."
This is not a request based on a doubt about whether she is faithful or not. It is a firm saying and asking Agni to be cool towards Hanuman. Agni had no other choice. He obeyed another agni (she is as pure as fire) and he was cool towards Hanuman. It felt as if ice was put on Hanuman's tail.
Another instance was Agni Pariksha. Sita Dev says this
yathā me hṛdayaṃ nityaṃ nāpasarpati rāghavāt |
tathā lokasya sākṣī māṃ sarvataḥ pātu pāvakaḥ || 6-116-25
karmaṇā manasā vācā yathā nāticarāmyaham |
rāghavaṃ sarvadharmajñaṃ tathā māṃ pātu pāvakaḥ || 6-116-27
"As I have never been unfaithful in act, thought and speech to Rama, who knows all the virtues, so let the fire-god protect me."
ādityobhavān vāyurdiśaścandrastathaiva ca |
ahaścāpi tathā sandhye rātriśca pṛthivī tathā || 6-116-28
yathānye'pi vijānanti tathā cāritrasaṃyutām |
"Since the adorable sun-god, wind-god, the four quarters and even so the moon-god, as also the deity presiding over the day-time and the twilights and the night and the earth and even others know me to be endowed with good conduct, so let the fire-god protect me."
She entered the fire blaze. Fire god protects her and she returns again safe and sound. Hence, not only Sita but everyone knew about the chastity of Sita Devi.