It sounds like I've been doing a bit of spring skiing, but you know I don't ski. The slopes I am referring to are the slopes of lines on graphs. As I work through Dr. Anton's calculus book's first chapters, I'm reviewing things I learned years ago. It seems amazing to me that I have already been at my math and physics learning program for more than five years. So, "back in 2002," which also sounds surreal to someone born in the mid-twentieth century, I studied graphs and linear equations and that basic high school algebra I suffered over when I was young.

What is new this time around is that in reference to calculus, it is pointed out to me that the slope of a line is also the tangent of the angle formed by that line and the X- axis of the graph. This is something I wondered about, believe it or not, when I was first re-learning graphs and linear equations. That is, I figured that the angle of the line had something to do with the math that put it there. But I didn't study trigonometry till "back in 2004," and the linear connection somehow wasn't made in all those books that I struggled with then.

But now the simple truth about the tangent is revealed to me. It's the ratio of rise over run, of y over or against x. In the right triangle formed by the line and the x-axis, it is the ratio of the triangle's sides that are opposite and adjacent to the angle made by the slope. It was something I should have seen as totally obvious, but the book had to point it out. And what's more, the relationship between the tangents of two sloping and intersecting lines is expressed in a trigonometric identity. These mind-numbing identities were what I was attempting to learn when I first started this Electron Weblog. I cannot claim that I am bright enough to remember any of them outright, but as soon as I was presented with one, I recognized it. That meant that I could go to my trigonometry book (the excellent Schaum's Outline) and review it. So finally, I encounter a use for at least one of those trigonometric formulas. I'm sure there will be plenty more.

Posted at 3:02 am | link