正弦 180 的值是 1.22465e-16 [英] Value of sine 180 is coming out as 1.22465e-16

问题描述

我想在 ios4 中实现一个正弦和余弦计算器:

I want to implement a Sine and Cosine calculator in ios4:

if([operation isEqual:@"sin"]){
    operand = (operand*M_PI/180.0);
    operand=sin(operand);
}

代码给出了从 0 到 90 值的正确答案.

The code gives me correct answer for values from 0 through 90.

当我给出 180 的值时，我得到 1.22465e-16 作为答案.我预计为零.

When I give value of 180, I get 1.22465e-16 as an answer. I expect zero.

这个小差异从何而来?

推荐答案

这是由于二进制数字系统无法准确表示 PI 造成的.

This is caused by the inability of a binary number system to exactly represent PI.

一种可能的解决方案是使用 sin 的对称性:

One possible solution would be to use the symmetry of sin:

sindeg(x) = sindeg(180 - x)

(或替代):

sin(x) = sin(M_PI - x)

将角度转换为范围 (-pi/2 : pi/2) 可减少近似误差.

Transforming the angle into the range (-pi/2 : pi/2) reduces the error of the approximation.

基本上:

if([operation isEqual:@"sin"]){
  operand = fmod(operand, 360);
  if (operand > 270) operand -= 360;
  else if (operand > 90) operand = 180 - operand;
  operand=sin(operand*M_PI/180.0);
}

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