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 upsidedown parabola with domain [2,2] because of the asin(x/2) and range [1,1] from the cosine.
Graphing the original expression on the TI83, TI84, and the HP50g, produced what was expected. However, the TI89 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.
