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

In my Trigonometric Applications class last Monday I gave them the questions to the reviewer for the test today, and I told them that if there was anything they did not understand about the lecture that they should ask it at that session because during the exam, if they happened to be in the class I would be proctoring, I would not answer any of their questions anymore.

I used the book that was also used in their Mathematical Methods 1 class last term. I wrote six problems on the board from the exercises in that text – three from conversion of trigonometric functions and three from proving of trigonometric equations.

The rest, I told them, which consisted of about fifty problems total, would be their assignment to be submitted next week. I also asked them when they want their free day. Overwhelmingly, they wanted it to be next week in anticipation of there being no classes on Monday. That would mean our next meeting would be on November 23.

Not surprisingly, they still weren’t able to finish those six items in the hour and a half long session. In some cases, they lacked the foresight to see how to simplify their expressions instead of prolonging them, and thus they ended up with complex fractions, radical signs and several additive terms, some in degrees two or greater.

They still had to submit what they had finished answering at the end of the class though, and they asked for the solutions again, just like for the last reviewer I gave them.

In my mechanics class in the afternoon, I discussed system of forces with friction on an inclined plane. For this one, instead of using the summation of forces along the two perpendicular axes in the horizontal and vertical directions, they had to decide if it is most advantageous to use the axes parallel and perpendicular to the inclined surface instead. This they had to discern from looking at which was more numerous: the forces that are vertical and horizontal or those that are not.

That meant deriving at the very least the weight, which is always downwards, to components in parallel and perpendicular directions. They had to get that from a right triangle in the illustration of the involved forces. Sometimes if the force is neither parallel nor perpendicular to the surface they had to get the components of that also.

At the very least the frictional force is already parallel to the surface and the normal force is already perpendicular.

In one of the examples I gave them, in fact, they could already see that the coefficient of friction is dependent only on the tangent of the angle of the inclined plane because the mass already cancels out. That was also one of the questions I placed in their quiz in the lab.

And that was our topic on friction. The next lesson is on conservation on mechanical energy already. This time though I seem to have enough sessions left in the term to discuss elasticity.

Tomorrow I’ll discuss the classes on Tuesday onwards, and I’ll be back on Tuesday next week. For now, this session is over.