Can't seem to find solution for vinyl tube to copper tube connection
Your most likely solution is to create the connector you need with two pieces - one to go from PEX (assuming that's what you have since Vinyl is not an approved plumbing material) to copper and one to go from 1/2" to 3/4".

When working with copper you generally have to sweat (aka solder) fittings, or less frequently screw them together (generally that's for end point connections like drop ears).

Lets start with what you need:

For your PEX connector, get a 1/2" to 3/4" PEX to female pipe thread connector (FPTC) 



and a 3/4" - 3/4" copper male threaded adapter



Be sure to get the copper adapter that will fit over the end of your copper pipe as some adapters are sized to fit inside other fittings while others are sized to receive pipe.  Test fit them in the store.

You will need to solder the 3/4" copper to the male threaded adapter.  See this video:

http://www.youtube.com/watch?v=doqoEJJOdYA

Note: 3-4 seconds of solder is too long.  Notice how much solder drips off of his fitting in that video.  That solder is molten metal and it will land on something.  1 second is plenty - you're looking for somewhere between 1/4 and 1/2" of solder to melt and vanish into the fitting.

Allow that fitting to cool completely (use a damp cloth to speed the process), then wrap silicone tape around the male threads.  Wrap in the direction of the threads, and only put about 2 layers of silicone over the threads.

Now very tightly screw the female to pex adapter onto the male threads.  Make this fitting as tight as you can using two wrenches - one to hold the pipe steady and the other to tighten the fitting.

Finally insert your pex tube firmly into the sharkbite fitting of your female connector.