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Hello and thank you for using justanswer. I want to be sure that I understand the question. You are asking if a professor needs to cite work which has a copyright in his teaching materials. Is this the gist of your question?
There is a great deal of information regarding this which I am happy to provide. However, your professor is in a different category than you are because he/she is using the information for educational purposes. As a teacher I play pretty fast and loose with copying work from a textbook and using it as illustrations in my instruction.
My concern upon reading your story is that you were dinged for using formulas created by someone else which is fine unless that was part of your assignment ... "create the formulas which will determine ... blah blah blah." As a student once, I used a small part of someone else's proof inside my proof (and shared it with many others) in a calculus class and although I was not accused of plagiarism the implication that the entire proof would be mine was there. Looking back, there was no one who claimed the proof, so it would have been hard to cite them. I found it in an obscure textbook.
As regards ***** ***** you sent, it does not seem that you were taking credit for the template.
How much do you want to know about this?