I was looking for some insight into the farewell greeting ta on The Urban Dictionary just now, and came across this mostly excellent top-ranked answer (adapted slightly, emphasis mine):
A slang word for "thanks."
The word is a result of the heavy Danish influence on the English language. Most people do not realize that the English language's roots are really Danish, in Jutland. Equipped with this knowledge this word is easy to decipher.
The Danish word for "thanks" is tak. In Scotland and upper England it was common to drop the at the end because of the way words were pronounced during the time of Old English and Middle English. Hence the slang word "ta" which should actually be pronounced "TA-k" but over time became "ta".
After reading that, I also remembered reading, when I was in our chat, that Frisian was the closest surviving spoken language to English, and then remembered the Wikipedia article stating that many Danish speakers are able to understand some spoken Frisian. With those facts, I hypothesized to myself that perhaps the Danes influenced both languages, before they had diverged, some very long time ago. Alas, that's all I can venture; though I know a fair bit about more modern influences on English — that is, Latin and Old French — I've haven't really seen this discussed before, which is no small wonder, as it seems that whatever influence the Danes had would have been ancient. It's also pretty strange, as compared to French, because Denmark is a bit aways from England; it's doesn't just have a narrow channel to cross, nor, if I remember correctly, doesn't share as intimately connected royal and noble lines as the French have with England.
So I guess my question is: Are the answerer's bolded words above correct? If they are, can someone offer a nice précis of how we can see this influence of the Danes, and how it came about?