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Learning:
The Journey of a Lifetime
A Cloud Chamber of the Mind

March 2006 Mathematics Notebook
Introduction      
Goals
   
     

An Example of a "Learning Process" Journal
Tuesday March 07, 2006
Learning Log Number 17
8:30 am Ballina NSW Australia

8:30 am Ballina NSW Australia

This is a continuation of my notes for "Calculus".

Continuation of Exercises For Section 1.3 [p. 64 - 66]

Yesterday I completed the first four exercises using Mathematica. I particularly enjoyed seeing a couple of the graphs as they were unexpected.

Many of the exercises involve a simple substitution of a value into an algebraic expression and are straight forward. However the trigonometric expressions require a clear understanding of the value of an expression for a particular angle. I need to do ALL of these manually and then confirm them with Mathematica.


19. . In words, what is the value of sin as the angle approaches p/2 (90 degrees)? Answer 1. This is confirmed with Mathematica.

20. . In words, what is the value of tan as the angle approaches p (180 degrees)?

Answer -1. Mathematica says 0. Of course!! It is (0 / (-1)).

21. . In words, what is the value of cos as the angle px approaches p.

Answer 0. Mathematica says -1. I am not doing very well with my trig this morning. I am mixing up my sides. I now see why the answer is -1.

22. . In words, what is the value of sin as the angle approaches p/2.

Answer 1. Mathematica says 1. Good.

Here are the results using Mathematica (Web, Mathematica). 9:20 am

Reflection: I am glad I decided to do all of the exercises involving trigonometric expressions as I clearly need to refine my thinking with these.

Difficulties: I am careless with the trig functions, confusing the various sides for an expression depending on which quadrant the angle is in. Not a serious problem, but one that requires me to be very careful.