program for calculation of the sine of an angle using the sine series

**Pulock2009** · 10-26-2013

hello everyone!
there seems to be some logical error in this program. i get unusually large values for any angle like even sine 90 degree.

Code:

/*c program to compute the sine series*/
#include<stdio.h>
#include<conio.h>
#include<math.h>

void main()
{
	  float x,sum=0,fraction=0;
	  int n,i,j;                /*the declarations*/
	  int factorial(int);

	  clrscr();

	  printf("\n Enter degree to calculate:");
	  scanf("%f",&x);          /*reading the angle to be calculated*/
	  printf("\n Enter number of terms:");
	  scanf("%d",&n);          /* upto how many terms to calculate the value*/

	  for(i=1,j=0;i<=n,j<n;i=i+2,j++)
	  {
			 fraction=pow(-1,j)*(float)(pow(x,i)/factorial(i));/*each term*/
			 sum+=fraction;       /* summing up*/
	  }

	  printf("\n sine(%f)=%f",x,sum);
	  getch();
}

int factorial(int n) /* the factorial calculating function*/
{
		int i;
		int fact=1;
		if(n==0)return 1;
		else
		{
			  for(i=1;i<=n;i++)
			  {
					  fact*=i;
			  }
                          return fact;
		}
		
}

please help!

**vart** · 10-26-2013

get rid of pow and factorial function

if you have calculated fraction on i-th iteration - next could be calculated rather simply using it.
something like

Code:

fraction = - fraction * x * x / i / (i-1);

FAQ > main() / void main() / int main() / int main(void) / int main(int argc, char *argv[]) - Cprogramming.com

conio.h is non-standard - get rid of it as well

**Salem** · 10-26-2013

> there seems to be some logical error in this program. i get unusually large values for any angle like even sine 90 degree.
Well yes, because the series usually take input as radians, not degrees.

So for 90', you would typically type in something like 1.57 (otherwise known as PI/2)

**megafiddle** · 10-26-2013

Even 90 radians should give a sin result between 0 and 1.

Isn't there a modulo function missing?

eg, angle = angle%90 (for an angle in degress)

Or is it supposed to be just one quadrant?

-

**tabstop** · 10-26-2013

Originally Posted by megafiddle

eg, angle = angle%90 (for an angle in degress)

-

That would imply that sin 100 = sin 10, which it doesn't.

The series expression for sin is only valid for radians, so if the end user is to type their input in degrees, the program will have to convert to radians before doing the series.

**megafiddle** · 10-26-2013

Thanks for the correction, that should have been angle = angle%360, plus you would need additional testing for quadrants.
My example was for degrees, as I believe those were intended to be the required input units.

The program above then, should limit input to 90 degrees or pi/2 radians?

-

**SirPrattlepod** · 10-26-2013

Originally Posted by megafiddle

The program above then, should limit input to 90 degrees or pi/2 radians?

I think the only thing that needs to be done is convert the input angle (in degrees) to radians because the Taylor series method for calculating sine uses radians and not degrees

**tabstop** · 10-26-2013

The series is good for all x. It will be quicker to converge for small x, but it will get there in the end.

**SirPrattlepod** · 10-26-2013

Originally Posted by tabstop

The series is good for all x. It will be quicker to converge for small x, but it will get there in the end.

That's correct, but if you enter 90 (degrees) the series isn't going to converge to the value of sin(pi/2) which is the answer the user is after...

Edit: Or am I missing something obvious?

**tabstop** · 10-26-2013

Originally Posted by SirPrattlepod

That's correct, but if you enter 90 (degrees) the series isn't going to converge to the value of sin(pi/2) which is the answer the user is after...

Edit: Or am I missing something obvious?

The programmer will have to do that conversion.

**SirPrattlepod** · 10-26-2013

I just noticed something else

Code:

for(i=1,j=0;i<=n,j<n;i=i+2,j++)

What does the expression i <= n, j < n evaluate to? Notice this is using the comma operator.

**SirPrattlepod** · 10-26-2013

Ok, I've fixed your code and there are several issues

a) If the user is inputting the angle in degrees the first convert their input to radians
b) See my previous post
c) Your method for calculating the sum of the series is wrong (note that terms should be either added or subtracted)
d) The factorial function is going to overflow very quickly; you may want to use different integer types; e.g. unsigned long factorial(unsigned n)
e) Even with the larger integer types factorial() is going to overflow very quickly; limit the value for 'n' that is acceptable

Suggestions
a) Fix the issues above
b) Put the code that calculates sine into a function (this will, for a start, make testing easier)
c) "Normalise" the angle to within the range 0 <= angle <= 2*pi radians so that the series converges faster AND mitigates the fact that you're going to have to limit 'n'

Further suggestions
a) Write a test function that compares the value of your sine function (you remembered to make it a function, right?) and the value that the math library gives for the same angle and checks that they are the same (given a reasonable error / precision)
b) You may be able to exit the summation loop early (e.g. if sum == previous_sum then there is no need to keep going on)

**grumpy** · 10-26-2013

Originally Posted by tabstop

The series is good for all x. It will be quicker to converge for small x, but it will get there in the end.

Not if done in software and any of the intermediate calculations overflow, it won't.

Once an integer overflow occurs (say, when calculating factorial()) or a floating point overflow occurs (say, when computing pow(90.0, i)) the game is over.

pow(90.0, i) will overflow for values of i over about 160 (some variation, depending on floating point representation).

Even worse, factorial(n) function will overflow a 16-bit int if n is greater than 7, and will overflow a 32-bit int if n exceeds 12. Even with long long ints (C99 or later) factorial() will overflow if n exceeds 20.

Apart from that, the series is for radians (as Salem said) and the termination condition of the loop is suspicious.

**SirPrattlepod** · 10-26-2013

Can someone ask grumpy to un-ignore me? :`-(

**SirPrattlepod** · 10-26-2013

Code:

      Angle     Expect        n=1        n=2        n=3        n=4        n=5        n=6   Err. n=6
     
          0    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
         10    0.17365    0.17365    0.17365    0.17365    0.17365    0.17365    0.17365    0.00000
         20    0.34202    0.34198    0.34202    0.34202    0.34202    0.34202    0.34202    0.00000
         30    0.50000    0.49967    0.50000    0.50000    0.50000    0.50000    0.50000    0.00000
         40    0.64279    0.64142    0.64280    0.64279    0.64279    0.64279    0.64279    0.00000
         50    0.76604    0.76190    0.76612    0.76604    0.76604    0.76604    0.76604    0.00000
         60    0.86603    0.85580    0.86630    0.86602    0.86603    0.86603    0.86603    0.00000
         70    0.93969    0.91780    0.94048    0.93968    0.93969    0.93969    0.93969    0.00000
         80    0.98481    0.94258    0.98681    0.98475    0.98481    0.98481    0.98481    0.00000
         90    1.00000    0.92483    1.00452    0.99984    1.00000    1.00000    1.00000    0.00000
        100    0.98481    0.85923    0.99419    0.98440    0.98482    0.98481    0.98481    0.00000
        110    0.93969    0.74047    0.95782    0.93875    0.93972    0.93969    0.93969    0.00000
        120    0.86603    0.56322    0.89905    0.86397    0.86611    0.86602    0.86603    0.00000
        130    0.76604    0.32218    0.82327    0.76185    0.76624    0.76604    0.76604    0.00000
        140    0.64279    0.01201    0.73786    0.63468    0.64324    0.64277    0.64279    0.00000
        150    0.50000   -0.37258    0.65227    0.48503    0.50095    0.49996    0.50000    0.00000
        160    0.34202   -0.83692    0.57824    0.31548    0.34394    0.34192    0.34202    0.00000
        170    0.17365   -1.38633    0.52991    0.12826    0.17737    0.17344    0.17366    0.00001
        180    0.00000   -2.02612    0.52404   -0.07522    0.00693   -0.00044    0.00002    0.00002
        190   -0.17365   -0.17365   -0.17365   -0.17365   -0.17365   -0.17365   -0.17365   -0.00000
        200   -0.34202   -0.34198   -0.34202   -0.34202   -0.34202   -0.34202   -0.34202   -0.00000
        210   -0.50000   -0.49967   -0.50000   -0.50000   -0.50000   -0.50000   -0.50000   -0.00000
        220   -0.64279   -0.64142   -0.64280   -0.64279   -0.64279   -0.64279   -0.64279   -0.00000
        230   -0.76604   -0.76190   -0.76612   -0.76604   -0.76604   -0.76604   -0.76604   -0.00000
        240   -0.86603   -0.85580   -0.86630   -0.86602   -0.86603   -0.86603   -0.86603   -0.00000
        250   -0.93969   -0.91780   -0.94048   -0.93968   -0.93969   -0.93969   -0.93969   -0.00000
        260   -0.98481   -0.94258   -0.98681   -0.98475   -0.98481   -0.98481   -0.98481   -0.00000
        270   -1.00000   -0.92483   -1.00452   -0.99984   -1.00000   -1.00000   -1.00000   -0.00000
        280   -0.98481   -0.85923   -0.99419   -0.98440   -0.98482   -0.98481   -0.98481    0.00000
        290   -0.93969   -0.74047   -0.95782   -0.93875   -0.93972   -0.93969   -0.93969    0.00000
        300   -0.86603   -0.56322   -0.89905   -0.86397   -0.86611   -0.86602   -0.86603    0.00000
        310   -0.76604   -0.32218   -0.82327   -0.76185   -0.76624   -0.76604   -0.76604    0.00000
        320   -0.64279   -0.01201   -0.73786   -0.63468   -0.64324   -0.64277   -0.64279   -0.00000
        330   -0.50000    0.37258   -0.65227   -0.48503   -0.50095   -0.49996   -0.50000   -0.00000
        340   -0.34202    0.83692   -0.57824   -0.31548   -0.34394   -0.34192   -0.34202   -0.00000
        350   -0.17365    1.38633   -0.52991   -0.12826   -0.17737   -0.17344   -0.17366   -0.00001

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program for calculation of the sine of an angle using the sine series

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