Everything that was used to create the Geogebra file involves knowledge that should be gained by a high school trig student.
(I am assuming that in the age of technology the concept of "phase shift" has become an integral part of a trig course.)
I did use the built-in tangent line function, rather than go through the task of using calculus operations to find the same result.
For those who want to see how the tangent line is actually identified, make sure to pay attention in your Calculus class.
As long as the notion of tangent lines is on the table, I suggest you take a look at this (the original is here)