By Sinéad Carew NEW YORK (Reuters) – The dollar index reversed course on Tuesday to rally sharply and U.S. stocks sank while Treasury yields climbed after data showed U.S. consumer prices rising faster than expected in August, prompting bets for more aggressive Federal Reserve rate hikes. Oil futures turned red after the Labor Department data on Tuesday showed that declining gasoline prices in August were offset by gains in rent and food costs. The Consumer Price Index gained 0.1% last month versus expectations for a 0.1% decline and after being unchanged in July. U.S. stock indexes had rallie…