Originally Posted by: wb.c Yeah, did some more reading and I guess since pi is only carried out to 16 decimal places (floating), the conversion from radians to degrees (pi/180) is limited by the 16 decimal place value of pi.
What isnât super clear is why it only happens with 270 degrees for cosine and 360 degrees for sine. Pi/180 is used to convert all input to angles.
Maybe at some point in my studies I learned why 270 degrees and 360 degrees are special, but I donât remember now.
Pi and more numbers are stored in computing machinery 40 decimals.
Not a single function exist in maths. They are approximated from the
4 basic arithmetic operations [+, -, *, /].
They are all normalized rational fraction P(n)/1+Q(n) on short range.
then like scaled. The coded native range is globally 21 floating point.
Error propagation brings down to around 18 floating point, by convention
15 digits are considered true to meet typical Abramowitz & Stegun.
Smath, Wolfram Alpha, Mathcad/PTC ... and else don't abide to the
convention of rounding smaller than 15 D to zero.
Mathcad 8, 2000, 2001i, 11 do round cos(270) = 0
In short, Smath does not calculate cos(270), trig and more exp, ln
are built-in in Windows. Smath and those more display the floating
point register, since when they broke the 15 D convention ?
Read more: Luke, Cody Junior, Hart et al.
round(cos((270),15)=0
Not built-in Windows from Smath menu ... Bessel, Airy ...
Have a good day ... Jean