Maybe I shouldn't have started this blog now, not with everything that's been going on.

Saturday I talked about Thursday. Today I’ll talk about Friday.

Up to a few minutes before my 1120am class started, when I was still in the cafeteria having an early lunch, I was of the mind that my lesson would be about getting the trigonometric functions of angles larger than 360 degrees or less than zero degrees expressed in radians.

This, I thought, would occupy about half of the session, then the other half would be used for explaining the “wrapping function”, making straight lines related to arcs, which I somehow neglected to teach last term but seems to be appropriate now with these students’ faster pace.

A subtopic of this, according to the chapter I was referring to in the textbook, would be the domains and ranges of the trigonometric functions, which would lead to graphing.

But before I went into the classroom I decided to go for verification and simplification of equations and expressions with trigonometric functions using identities.

For the 1120am class I gave their exercise at the start of the class, just to be able to see who were those who showed up late from having an extended lunch.

While they were solving that I already wrote on the board the derivation of the reciprocal and ratio identities, based on the fraction definitions of the trigonometric functions.

Afterwards I derived the Pythagorean identities. I told them that since these were the simplest and mostly used identities in verification and simplification, that it is expected for them to memorize these, or at least know how to get to them from the familiar formulas. I also gave a hint that the later and more complicated identities would be given in the exams.

I also listed down the tips in verification, which are to end up with either an expression of equality or a known identity, simplify the more complex side of the equation first, and to convert to one or two trigonometric functions first.

As a practice to this last suggestion we took up expressing certain functions in terms of other functions, such as tangent in terms of cosine (it is equal to the square root of one minus cosine squared all over cosine).

We started out with simple examples, addition of two terms, simple products and fractions. Next meeting I’ll give them more complex equations to verify.

In the 1pm class, I challenged them to settle an unofficial bet we had among the faculty who would perform better, those who hadn’t had lunch (the earlier class) or those who had (them).

For their class I also started with conversion/expression and simplification first before going to verification, and I asked them what kind of problem they wanted for their end of period exercise: they chose conversion, but realized in the midst of the deceptively simple expression that conversion was somewhat easier because they knew when it would end: with an equality, which was not the case with conversion. They had doubts whether something they solved was in simplest form already or not.