Why Check engine tiburon 2003?

could be many things, however what I found to be the problem on mine, was the gas cap

if the gas cap is not on properly, the HVAC system of the vehicle goes nuts and creates a "CHECK ENGINE" light

give it a try, after a few cold starts it will reset itself and the light will go off,

if you have a code reader this also helps to troubleshoot and get the light off