sin(2*pi) vs sind(360)
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Could someone please explain to me why sin(2*pi) gives me non-zero number and sind(360)? Does this have to do with the floating points of pi?
回答（3 个）
Mike Croucher
2022-10-21
2 个投票
If you ever need to compute sin(x*pi) or cos(x*pi), its better to do sinpi(x) or cospi(x). You never explicitly multily x by a floating point approximation ot pi so you always get the results you expect.
Yes, it is because π is a value that cannot be represented precisely using a finite binary floating point number. This is also shown in the sind documentation:
"Sine of 180 degrees compared to sine of π radians"
sind(180)
ans =
0
sin(pi)
ans =
1.2246e-16
2 个评论
david dang
2015-7-13
No.
Unless of course you buy a computer with infinite memory to hold an infinite representation of π and yet can somehow perform operations at the same speed as your current computer.
π is an irrational number. How do you imagine representing an irrational number with a finite floating point value and not getting rounding error? All numeric computations with floating point numbers include rounding errors, and it is your job to figure out how to take this into account. To understand floating point numbers you should read these:
Walter Roberson
2015-7-13
0 个投票
Yes, it is due to pi not being represented precisely due to the fact that floating point representation is finite.
2 个评论
david dang
2015-7-13
Torsten
2015-7-13
For a numerical computation, sin(pi)=1.2246e-16 should be exact enough.
Best wishes
Torsten.
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