Math.cos（90 * Math.PI / 180）为什么产生6.123031769111 ...而不是零？ [英] Why does Math.cos(90 * Math.PI/180) yield 6.123031769111... and not zero?

问题描述

我将度数转换为弧度（degree * Math.PI / 180），但为什么会出现下列情况：

  Math.cos （90 * Math.PI / 180）
  

产量6.123031769111 ...而不是零？

我试图使用矩阵来执行二维旋转，结果完全没有成功。

解决方案

  Math.cos（90 * Math.PI / 180）
  

是

  6.123031769111886 e-17 
  

注意 e-17 最后，这意味着这个数字是6.123 x 10 -17 。这是一个非常接近0的数字，它实际上是0.它不是0的原因是由于IEEE-754双格式中的四舍五入错误，导致你无法精确地表达出π / 2，并在余弦的计算中产生细微的舍入误差。顺便说一句 - 当结果以6开始时，我感到非常惊讶！只有当我看到事情开始变得有意义了。

希望这有助于您！

I convert degrees to radians (degrees * Math.PI/180) but why does the following:

Math.cos(90 * Math.PI/180)

yield 6.123031769111... and not zero?

I'm trying to perform 2D rotations uses matrixes and the results are completely out of whack.

解决方案

The output of

Math.cos(90 * Math.PI/180)

is

6.123031769111886e-17

Notice the e-17 at the end, which means that this number is 6.123 x 10^-17. This is a number so vanishingly close to 0 that it's effectively 0. The reason that it's not identically 0 is due to rounding errors in the IEEE-754 double format which prevents you from getting an exact representation of π / 2 and causes minute rounding errors in the calculation of the cosine.

By the way - I was pretty surprised as well when the result came back starting with a 6! It's only after I looked at the very end that things started to make sense.

Hope this helps!

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