The Museum of HP Calculators

HP Forum Archive 17

 Graphing Calculator Error (interesting)Message #1 Posted by Chuck on 19 Sept 2007, 4:47 p.m. Today I had my students find an algebraic expression for `cos[2 asin(x/2)]` It turns out to be `1-(x^2)/2` an upside-down parabola with domain [-2,2] because of the asin(x/2) and range [-1,1] from the cosine. Graphing the original expression on the TI-83, TI-84, and the HP50g, produced what was expected. However, the TI-89 produced the entire parabola!!! Whoops. My guess is the 89 did a little internal simplification, or the CORDIC method employed is different than the other calculators. It would be interesting to see what other calculators give.... Interesting-- Mathematica 6.0 gives the entire parabola as well. Guess I'll need to investigate a little more. [--addendum--] I think I know why: asin[x] where |x|>1 gives a complex result. Therefore, allowing a complex domain (TI89 and Mathematica) for cos[x] gives a range beyond [-1,1]. I'm sure I new that at one time, but my complex analysis class was over 20 years ago. Interesting. CHUCK Edited: 19 Sept 2007, 5:02 p.m.

 Re: Graphing Calculator Error (interesting)Message #2 Posted by Chuck on 19 Sept 2007, 5:23 p.m.,in response to message #1 by Chuck I was correct. I pulled out my complex analysis book (1987 Marsden) and rediscovered the complex definition for sine and cosine (they look similar to the defs for cosh and sinh). On a similar note: solve the equation sqrt(1-x) = sqrt(3-2x) The REAL solution is x=2. However, the graphs do not REALly interesect (though in the complex world they do, at 0+i). A conundrum.

 Re: Graphing Calculator Error (interesting)Message #3 Posted by Jandro Kirkish on 19 Sept 2007, 7:45 p.m.,in response to message #2 by Chuck Maple 11 also gives the entire parabola.

 Re: Graphing Calculator Error (interesting)Message #4 Posted by Meenzer on 20 Sept 2007, 1:23 a.m.,in response to message #1 by Chuck The Casio fx-7400G+ and the HP 48G draw from -2 to 2. GeoGebra and Graph as well. Edited: 20 Sept 2007, 1:32 a.m.

 Re: Graphing Calculator Error (interesting)Message #5 Posted by sjthomas on 20 Sept 2007, 2:34 a.m.,in response to message #1 by Chuck Both the TI-nspire CAS and the Casio fx-9860G Slim graph the parabola segment from x = -2 to x = 2.

 Re: Graphing Calculator Error (interesting)Message #6 Posted by Chuck on 20 Sept 2007, 1:14 p.m.,in response to message #5 by sjthomas Hmm, I would have expected the nspire to give the entire parobola. Interesting what these different devices and programs give. For those interested, I graphed the entire arcsine function using and x-y-i coordinate system with the standard x-y axes and the imaginary pointing straight out. The result was the standard arcsine on the vertical x-y plane of x:[-1,1] and then the complex part on a plane pi/2 high traveling in the imaginary directions. Here's a link to what I got Mathematica to do. Now I need to write a program for the HP-35s to give these complex results instead of the "Invalid Data" error. CHUCK

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