Solution 10702: Unexpected Results When Sin(Pi) Does Not Return Zero on the TI-68.
Why does the TI-68 not give zero when calculating the sin(pi)?
The answer displayed when calculating p radians is an approximation of zero. When solving trigonometric functions, very sophisticated algorithms are used to calculate the most accurate answer possible.
With this in mind, plus the fact that it uses a 13-digit approximation of the irrational number p, the TI-68 is calculating the correct answer. Since the value of p is in error in the 13th digit, some results using that value will also be in error in the 13th digit.
Some calculators use rounding scheme to generate the expected zero answer. This has the potential to create problems in some types of calculations. Therefore, TI decided to use no rounding schemes on the TI-68.
Please see the TI-68 guidebook for additional information.