c – Sin和Cos为众所周知的角度给出意想不到的结果

我确信这是一个非常愚蠢的问题,但当我向c / c的cos()和sin()函数传递180度的角度时,我似乎收到了一个不正确的值.我知道它应该是：
sin为0.0547,cos为0.99
但我得到了3.5897934739308216e-009的罪和-1.00000的cos

我的代码是：

double radians = DegreesToRadians( angle );
double cosValue = cos( radians );
double sinValue = sin( radians );

DegreesToRadians()是：

double DegreesToRadians( double degrees )
{ 
    return degrees * PI / 180; 
} 

谢谢 ：)

解决方法:

C/C++提供sin(a),cos(a),tan(a)等需要具有弧度单位而不是度数的参数的函数. double DegreesToRadians(d)执行转换,该转换接近但转换结果四舍五入为近似值.机器M_PI也接近,但与数学无理π的值不同.

OP的代码180传递给DegreesToRadians(d)然后传递给sin()/ cos()给出的结果与舍入,double()的有限精度和PI的弱值可能不同于预期.

一种改进是在调用trig函数之前以度为单位执行参数减少.下面将角度首先降低到-45°到45°范围,然后调用sin().这将确保sind中的大值N(90.0 * N) – > -1.0,0.0,1.0. .注意：sind(360.0 * N / – 30.0)可能不完全等于/-0.5.需要一些额外的考虑.

#include <math.h>
#include <stdio.h>

static double d2r(double d) {
  return (d / 180.0) * ((double) M_PI);
}

double sind(double x) {
  if (!isfinite(x)) {
    return sin(x);
  }
  if (x < 0.0) {
    return -sind(-x);
  }
  int quo;
  double x90 = remquo(fabs(x), 90.0, &quo);
  switch (quo % 4) {
    case 0:
      // Use * 1.0 to avoid -0.0
      return sin(d2r(x90)* 1.0);
    case 1:
      return cos(d2r(x90));
    case 2:
      return sin(d2r(-x90) * 1.0);
    case 3:
      return -cos(d2r(x90));
  }
  return 0.0;
}

int main(void) {
  int i;
  for (i = -360; i <= 360; i += 15) {
    printf("sin()  of %.1f degrees is  % .*e\n", 1.0 * i, DBL_DECIMAL_DIG - 1,
        sin(d2r(i)));
    printf("sind() of %.1f degrees is  % .*e\n", 1.0 * i, DBL_DECIMAL_DIG - 1,
        sind(i));
  }
  return 0;
}

产量

sin()  of -360.0 degrees is   2.4492935982947064e-16
sind() of -360.0 degrees is  -0.0000000000000000e+00  // Exact

sin()  of -345.0 degrees is   2.5881904510252068e-01  // 76-68 = 8 away
//                            2.5881904510252076e-01
sind() of -345.0 degrees is   2.5881904510252074e-01  // 76-74 = 2 away

sin()  of -330.0 degrees is   5.0000000000000044e-01  // 44 away
//  0.5                       5.0000000000000000e-01
sind() of -330.0 degrees is   4.9999999999999994e-01  //  6 away

sin()  of -315.0 degrees is   7.0710678118654768e-01  // 68-52 = 16 away
// square root 0.5 -->        7.0710678118654752e-01
sind() of -315.0 degrees is   7.0710678118654746e-01  // 52-46 = 6 away

sin()  of -300.0 degrees is   8.6602540378443860e-01
sind() of -300.0 degrees is   8.6602540378443871e-01
sin()  of -285.0 degrees is   9.6592582628906842e-01
sind() of -285.0 degrees is   9.6592582628906831e-01
sin()  of -270.0 degrees is   1.0000000000000000e+00  // Exact
sind() of -270.0 degrees is   1.0000000000000000e+00  // Exact
...

标签：c,trigonometry,cmath
来源： https://codeday.me/bug/20190917/1809581.html