Roughly as frequent as English this/that, but with higher preference for ten/ta/to over tamten/tamta/tamto compared to English – there are many instances where English that can be translated as tan/ta/to, although I'm not sure what is the interpretation the creators of the course went with.
Roughly as frequent as English this/that
Maybe even more, because it may also replace the English "the".
"there are many instances where English that can be translated as tan/ta/to"
I'll use some quotes from Discworld series, both English original and official translations, with "that" used both as a pronoun and a determiner:
That's what's so stupid about the whole magic thing, you know.
To właśnie jest głupie w tej całej magii.
“In a figurative sense,” he said.
“What does that mean?
“Well, it means no,” said Cutwell.
– W sensie metaforycznym - mruknął mag.
– Co to znaczy?
– No więc... To znaczy, że nie.
"I like the idea of democracy. You have to have someone everyone distrusts," said Brutha. "That way, everyone's happy."
- Podoba mi się idea demokracji - stwierdził Brutha. - Trzeba mieć kogoś, komu nikt nie ufa. Dzięki temu wszyscy są zadowoleni.
And one day people will say: why didn't they sort it all out, back then? On the beach. Before it all started. Before all those people died. Now we have that chance. Aren't we lucky?
Aż pewnego dnia ludzie zapytają: Dlaczego wtedy nie załatwili tych spraw? Na plaży? Zanim wszystko się zaczęło? Zanim zginęło tylu ludzi? Teraz mamy tę szansę. Czyż nie sprzyja nam szczęście?
Fingers-Mazda, the first thief in the world, stole fire from the gods. But he was unable to fence it. It was too hot. He got really burned on that deal.
Palcy-Mazda, pierwszy złodziej na świecie, wykradł bogom ogień. Ale nie mógł go sprzedać, bo towar był zbyt gorący.Mocno się sparzył na tym interesie.
Wait, why is it not tą here? I think in an earlier sentence with a noun that had -ę in the accusative, it was tą and not tę? Or do I remember wrong?
While ten/ta/to follows adjective-like declension patterns, it's the exception in the feminine accusative singular, which would take -ą according to the pattern, but takes -ę here.
Feminine singular instrumental takes -ą as expected.
I believe tę is Accusative (fem.) and tą is Instrumental (fem.), so in this case tę
because accusative of ta is "tę".
If you heard Polish people use tą- it is a common mistake.
It would be "I like that water", not "I like this water".
tę/tę/tamtą = this/that/that
No, it's only for liking, and not even all kinds of it.
The other verb used to describe liking is podobać się, which is used in a reverse way, like Russian нравиться or Spanish gustar. Lubić refers to liking something on a deeper level, podobać się refers to liking something for more superficial reasons. Lubić refers to a bond between subject and object, podobać się refers to (some kind of) attractiveness of the subject to the object.
I won't give you any examples though, it's a lot of work, it's complicated and I don't feel I'm capable of explaining it more clearly.