PROBLEM WITH PI π

[Wes Loewer]

Short Answer:
If your firmware version is not too old (2020-05-11 or later), go to the Home Settings and turn on Intelligent Math. With the latest firmware (2023-04-13) the result you want is the default behavior even without Intelligent Math turned on.

Longer Answer:
The Prime is essentially two calculators in one. The CAS is a symbolic calculator which can perform exact calculations, while Home is a numeric calculator which gives decimal approximations. In CAS, sin(π)=0 because π is exactly π. In Home, however, π is approximated as 3.14159265359. Since sin(3.14159265359) = −2.06761537357ᴇ−13, this is the "correct" answer. (If you enter =sin(PI()) in a spreadsheet and you will also get a non-zero answer, although you might have to set the format to Scientific in order to see it.)

Calculator manufacturers have to choose between two philosophies. Do you tell the truth and give the actual calculated value? Or do you lie and give people what they expect? Traditionally, HP calculators have given the actual calculated value while TI and Casio calculators have given people what they expect. On the TI and Casio numeric calculators, π is approximated as 3.1415926535898. The actual value of sin(3.1415926535898) is -6.98ᴇ-15, but these calculators typically give 0.

Computer scientist and engineers who concern themselves with numerical methods and error analysis would typically prefer to see the actual calculated value while math students typically prefer the expected answer. As the latter group is now the target customer, it makes sense that hp branded calculators have made the switch to giving the "expected" value.

Basically, people prefer to be lied to. People can't handle the truth. :-)