2014-05-05 / 2014-W19-1T18:36:45-05:00 / 0x5368208dI enjoy finding calculations that I would consider reasonable for my students to perform that their calculators cannot.
Using a double-angle identity and the pythagorean identity, it’s pretty straightforward to show that \(\sin\left(2\sin^{-1}\left(-\frac{4}{5}\right)\right) = -\frac{24}{25}.\) However, my TI-89 returns an unhelpful \(-\sin(2\sin^{-1}(4/5))\) instead.
Amusingly, the calculator does know that \(2\sin\left(\sin^{-1}\left(-\frac{4}{5}\right)\right)\cos\left(\sin^{-1}\left(-\frac{4}{5}\right)\right) = -\frac{24}{25}.\)
(My calculator is running the 2005 version of the software. It’s possible this has been fixed since then.)