The question is:
math.stackexchange.com/questions/501660/is-there-a-way-to-get-trig-functions-without-a-calculator
This following answer is quite vauge and I do not think I can develop it further alone, but it may it be of some help, should I post it as an answer?
Where $A$ and $B$ are vectors, and $x$ is $A ∠ B$.
$A · B = |A| |B| cos(x)$
This uses trigonometry, however the following definition achieves the same result without using trigonometry: