rejoicing vs triumphal

rejoicing is a noun but triumphal is not a noun.

Word	Noun	Adjective	Verb	Adverb
rejoicing	Yes	Yes	No	No
triumphal	No	Yes	No	No

As adjectives, rejoicing and triumphal are synonyms defined as:

rejoicing and triumphal: joyful and proud especially because of triumph or success

Other synonyms of rejoicing include exultant, exulting, jubilant, prideful, triumphant.

rejoicing (noun)	triumphal (noun)
the utterance of sounds expressing great joy
a feeling of great happiness

rejoicing (adjective)	triumphal (adjective)
joyful and proud especially because of triumph or success	relating to or celebrating a triumph
	joyful and proud especially because of triumph or success