|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
It turns out to be
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.
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.
Edited: 19 Sept 2007, 5:02 p.m.