The rupee appreciated 6 paise to 83.30 against the US dollar in early trade on Tuesday, supported by a firm trend in domestic equities. At the interbank foreign exchange market, the local unit opened at 83.37 against the greenback. It later touched 83.30 in initial trade, registering a rise of 6 paise from its previous close. On Monday, the rupee appreciated by 8 paise to close at 83.36 against the US dollar. "There has been no adverse geopolitical development in the last 24 hours and that has helped restore some confidence and improved market sentiment," IFA Global Research Academy said in a research note. "Markets are looking forward to earnings from US' big tech companies and if they meet or beat expectations, we could see risk sentiment remain stable for some time despite elevated US yields," the note said, adding that the rupee is likely to trade in 83.25-83.40 range with sideways price action. Meanwhile, the dollar index, which gauges the greenback's strength against a baske