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

Going back to my account of my Trigonometric Applications class last Monday, I first showed the students the graphs of all six trigonometric functions.

For the four other than sine and cosine, I had to show them both the large view (from negative two times ten raised to the sixteen to positive one times ten raised to sixteen – the closest approximation the table of values and graph could give for negative to positive infinity) and the zoom in from negative four to positive four, both vertical borders, this was just to show that tangent was “complimentary” to cotangent, and secant with cosecant. Hopefully they realized why these functions had “co” in their names.

From there we concentrated on the sine and cosine functions, and how the graphs would change if a variation of coefficients that could be part of the single function equation. This was then translated to the five properties that define the dimensions of the graph: minimum and maximum values, amplitude, period and y-intercept, which is technically the phase shift or phase difference for engineering students studying electrically generated or represented waves.

One student, who, according to my co-teachers in fact still employs the same tutor she had in high school, asked me if the topic we were discussing is in the textbook.

I told her, yes, but not in the same context. The book really wants the students to know not only to graph all trigonometric functions, but also equations involving more than one trigonometric function. A simple task involving one click of the mouse for students who have access to spreadsheet software and other similar drawing tools. Better, I concluded, to let the students know what those attributes of the graphs meant.

Since there were four coefficients and added constants that varied the appearance of the graph, I also had the students determine which numeric value affected which property.

From there it was a quick segue to inverse trigonometric functions. This time, instead of letting the students fill tables on the board showing the range of values of angles that are given by their calculator as the inverse sine, cosine and tangent functions, the tables were automatically filled in by the spreadsheet software. Yeah, removing it from their computation brought it one step closer to abstraction, but that’s what the computer projection was for.

To make sure everyone participated I just reminded them how to get the same results as the table in their calculator, which depends on the model, similar to what I did in the MM1 class.

Inverse sine, for instance, only returns angles from negative ninety to positive ninety, which translates to the first and fourth quadrant. So if they know the angle they are looking for is in either the second or fourth quadrant then they have to convert the result to the equivalent value in the correct quadrant.

That’s all for today. I’ll resume the discussion next time. Class dismissed.