Chapter 2 of the Banner book is a review of trigonometry. I can use such a review. I also want to have a first look at a book I bought last week, "Mathematica Demystified". I want to be able to move easily between conventional material and cyborgian efforts.

• "To do calculus, you really need to know trigonometry." [p. 25]

That is pretty clear.

• "The first thing I want to remind you about is the notion of radians. Instead of saying that there are 360 degrees in a full revolution, we'll say there are 2p radians. ... there is a reason: the circumference of a circle of radius 1 unit is 2p units. Thus, the arc length of a wedge of this circle is exactly the angle of the wedge." [p. 25]
  
  
• "... the main thing is to be comfortable with the most common angles in both degree and radian form." [p. 25]

Got it.

• Banner then provides a table of the values for the sine, cosine and tangent of the 5 most common angles (0, 30, 45, 60 and 90 degrees). ... "Please, please, I beg of you, learn this table! There are few things worth memorizing and this table is one of them." [p. 28]

The next few pages provide an excellent description of the basic relationships as the angle varies between 0 and 2p. Now to sit back and read this material slowly and carefully, making sure that it makes sense and that I understand it.

 

I switched to hand-writing to clarify my ideas about various angles and triangles. It is much easier to sketch a graph than it is to figure out how to do it with web-based technology. I am definitely feeling pleased with myself this morning. This is math that I have not touched in over 40 years. Total time this morning: about 2 hours.

Tags: mathematics, calculus