sine of an angle in degree mode

[Thomas Okken]

(01-24-2018 12:37 PM)rflesch Wrote:  how does the algorithm used in a calculator 'know' that it's exactly zero.

The same way the algorithm "knows" the result for any argument: by performing a calculation. Plug in a number, perform a series of steps, and hey presto, you have a result. Take a sine algorithm, plug in zero, you get zero. That's all there is to it, what else were you thinking of?

Now, a sine algorithm might recognize zero, treat it as a special case, and return zero immediately, rather than going to the usual sequence of steps. If you want to call that "cheating," go right ahead, but most of us would call it a performance optimization: same result, only faster.