I have the answer
OK, If you are using a cable ore satellite receiver before the TV you should find RCA outs on that box, but from the your description it sounds like you have cable or antenna going straight into the TV, with no receiver box, and therefore no RCA outs.
The answer! (Ok, I’ll admit this is a bit archaic.)
Do you remember those things from the late `80s and throughout the `90s, what was it called? You stick a huge rectangle of plastic into a slot and a fuzzy movie appears on the screen...Oh yeah, a VCR!!
But really plug your cable into the co-ax in and another cable from the co-ax out into your TV, then you can use the RCA outs from the VCR to carry audio to your stereo system. The only real drawback is that you have to switch channels on the VCR and leave the TV on Chan 3 or video in if you use the RCA video out from the VCR.