为什么 Math.cos(90 * Math.PI/180) 产生 6.123031769111... 而不是零?

2022-01-14 00:00:00 geometry math trigonometry javascript

我将度数转换为弧度(度数 * Math.PI/180)，但为什么会这样:

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

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

产量 6.123031769111... 而不是零?

yield 6.123031769111... and not zero?

我正在尝试使用矩阵执行 2D 旋转，结果完全不正常.

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

推荐答案

输出

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

是

6.123031769111886e-17

注意末尾的e-17，表示这个数字是6.123 x 10^-17.这是一个非常接近 0 的数字，实际上它是 0.它不完全是 0 的原因是由于 IEEE-754 双精度格式中的舍入错误，这会阻止您获得 π 的精确表示./2 并在余弦计算中导致微小的舍入误差.

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.

顺便说一句 - 当结果以 6 开头时，我也很惊讶！直到我看到最后才开始明白事情的意义.

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.

希望这会有所帮助！

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