When I pass an angle of 180 degrees into C/C++'s cos() and sin() functions, I appear to receive an incorrect value. I know that it should be:
But, I get:
My code:
double radians = DegreesToRadians(angle);
double cosValue = cos(radians);
double sinValue = sin(radians);
DegreesToRadians():
double DegreesToRadians(double degrees)
{
return degrees * PI / 180;
}
C/C++ provides sin(a), cos(a), tan(a), etc. functions that require a parameter with radian units rather than degrees. double DegreesToRadians(d) performs a conversion that is close but an approximate as the conversion results are rounded. Also machine M_PI is close, but not the same value as the the mathematical irrational π.
OP's code with 180 passed to DegreesToRadians(d) and then to sin()/cos() gives results that differ than expected due to rounding, finite precision of double() and possible a weak value for PI.
An improvement is to perform argument reduction in degrees before calling the trig function. The below reduces the angle first to a -45° to 45° range and then calls sin(). This will insure that large values of N in sind(90.0*N) --> -1.0, 0.0, 1.0. . Note: sind(360.0*N +/- 30.0) may not exactly equal +/-0.5. Some additional considerations needed.
#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;
}
Output
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
...