Euler Identity in Home

[ColinJDenman]

Quote:EDIT: To address your specific example of: \( \frac{\cos(\pi/2)}{\sin(\pi)} \) -- there is a singularity at \( \theta = \pi \) for \( \frac{\cos(\theta/2)}{\sin(\theta)} \) so any numerical answer your calculator returns is the wrong answer.
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I recommend reading:

http://www.stewartcalculus.com/data/ESSE...mp_stu.pdf
http://apcentral.collegeboard.com/apc/me...11703.html
http://www2.edc.org/cme/showcase/KY/calcliesarticle.pdf

(The third link is extremely interesting -- the graph of \( \sin(46x)\) looks like \(-\sin(x)\).)

I do entirely agree that returning a value is wrong. It should say divide by zero, or not a number or "I'm sorry Dave, I can't do that" or some other indicator. I favour the approach that the calculator tells you that your going near its limitations rather than giving a value that can potentially roll through into further calculation. I liked this example because it is a) obviously wrong and b) too big to justify as a small thing like the 2E-13 stuff.

If you wish, "a calculator's gotta know its limitations". Or I need a shotgun:
http://www.hpmuseum.org/forum/thread-1103.html

Your references are indeed interesting. Thanks.