tan(pi/2)=-195948537906 (?)

[Joe Horn]

(06-09-2020 01:51 PM)pinkman Wrote:  HP15C -> -4878048780
HP35s -> -195948537906
HP49g+: -195948537906 (or infinite symbol if CAS / Approx is unchecked)
Free42 (iOS): -1,79243... E33
WP34s (iOS): 1,6149... E15

It's a resolutely numerical approach.

HP's philosophy is very different from other calculator manufacturers:

"Our users know what they're doing and know how to use the tool in their hand. The numbers that they input to any function are exactly what they intended to input, to the last digit. We do the same with the output. We show ALL the digits. We don't cheat by hiding several digits behind the euphemism of 'guard digits'. So if a user presses the PI key, we assume that the user knows that the result is not the infinite number of digits of pi, nor is it a result whose last few digits are a secret. The user is smart enough to know that pressing PI on an HP 12-digit-mantissa machine yields exactly 3.14159265359, no more and no less. If the user then divides by 2 and then presses the TAN key in radian mode, we assume that the user wants the tangent of exactly the number of radians in the display, and we return all the digits of the result rounded to 12 significant digits. On HP calculators, what you see is exactly what you have."

TI's philosophy is, "We assume that the user is an idiot who thinks that pressing the PI key actually returns exactly pi. Furthermore, if they then divide it by 2 and take the TAN in radian mode, we catch that particular case and we ASSUME that we know better than the user does, and we return what WE think that the user PROBABLY expects. We also display fewer digits than are calculated, hiding the roundoff errors behind 'guard digits' so that nobody is confused when they get nasty EXACT results like HP gives."

It's not a matter of who is right or which philosophy is better. It's a matter of knowing how your tools work and using them accordingly.