As it happens with so many words, the belief or reliance on the veracity, integrity, good will, or other virtues of someone has two different terms in English. Both of them are Indo-European in origin. One of them has Germanic roots. “Trust” comes from Old Norse traust, which derives from Proto-Germanic *traustam < * treuwaz, which in the end has its source in the Proto-Indo-European (P.I.E.) root *deru “be firm, solid, steadfast.”
The other word, “confidence,” has Latin origin. It comes either from Old French confidence or directly from Latin confidentia, which in the end is a compound word: com is probably an intensive prefix—namely, a word that gives more emphasis—and fidere means “to trust.” The source of fidere is one of those P.I.E. roots that do not look at all like their descendent to the untrained eye: *bheidh “to trust, confide, persuade.” Let’s not forget, however, that there are more than a couple of thousand years between the Latin word and the putative P.I.E. root. (To be remembered: the words with an asterisk are not directly attested, but it is supposed that they have existed on the basis of comparative evidence.)
Of course, since the concept is one, there is one Armenian word for both English terms: վստահութիւն (vustahootyoon). Armenian, like French or Spanish do at times, combines an adjective with a suffix to yield the corresponding noun. Here, վստահ (vustah “sure; reliable; daring”) comes into play with the suffix – ութիւն (ootyoon) . If you want the verb, you just need to put together vustah and the desinence –իլ (il) to obtain վստահիլ (“to trust”).
Do not be surprised: vustah is attested in Classical Armenian and has Iranian origin. It is derived from Pahlavi (the Iranian dialect spoken by the Parthians, from which the Arshakuni family came) vistaxv “sure, reliable, daring; insolent.” Of course, someone who is daring may become insolent in the absence of self-control. But the Armenian language borrowed the word vustah without keeping that meaning. When you are vusdah, you are basically sure or confident about something, or you trust someone.
Of course, in God we trust. However, there are people around you who also deserve your trust. It is a good virtue to practice vustahootyoon.