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Every IEEE-754 Binar圓2/64/128 value can be exactly represented as a decimal number. Eg.: * on the HP42S sim., sin(1000*pi) ~ 115.8.E-33 * on the HP48G+: ~2.067.E-10 * same on the HP39gII * what do you get with your own calc? Which one is closer to zero?) If you want exact values, use symbolic calculators. And as we just saw, why care if it gives sin(pi)=0 but sin(n*pi) != 0? (So to get an idea about "precision" of a given calc, try sin(n*pi) with n a large integer. Just because a given calc doesn't implement sin() this way, doesn't mean it's bad. But try a multiple of pi, and see how even on those calcs, the result will not be zero anymore. Then obviously sin(pi) would be sin(pi-pi)=sin(0)=0. The most common reason why you'd get zero is if sin(x) is computed modulo pi (the exact same numeric constant as the pi it gives you when you press 'pi') and the sign handled separately. While sin(pi), with pi an approximation of pi, should never be exactly zero for an infinitely precise sin() function, for an implementation with finite precision, everything goes. As we explained in this thread, this has nothing to do with precision, but everything to do with how the sin() function is implemented.
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My 48G+ gives 0 for sin(pi), but not my other HP calc (HP39gII which is kind of a simplified predecessor of the Prime), nor the HP42S simulators. I have 2 physical HP calcs, and a few emulators. Some calculators happen to give exactly zero for sin(pi) (using the 'pi' constant provided by the calculator itself), while others don't. We all agree (except commie apparently) that precision has nothing to do with it, since pi itself can only be an approximation. To finally add a little point about this all, regarding the sin(pi) != 0 affair in itself.