Maclaurin series Sine(x) function Expantion

[hummingdev]

Hi guys hope you're doing well
so this is my assigment
Maths3assignment2-no3 (2).pdf

this is as far as I got in the code, problem is I'm not getting the same accuray for the output for the program, in comparison with a calculator.

also I'm trying to display each iteration of the accuray for the output but I think that's wrong as well for e.g.

-----------------------------------------
ITERATIONS -------- value
-----------------------------------------
ITERATION 1 -------: 2.500000
ITERATION 2 -------: 2.750000
ITERATION 3 -------: 2.625000
ITERATION 4 -------: 2.687500
ITERATION 5 -------: 2.718750
....
....
....
ITERATION 20-------: 2.740645

and so on..

I had a read of

http://blogs.ubc.ca/infiniteseriesmodule/units/unit-3-power-series/taylor-series/maclaurin-expansion-of-sinx/

but no luck .. you're gudince is my only help

thank you

/* PROGRAM FOR SUM OF SIN (X) SERIES *//*x -x^3/3! + x^5/5! - .........*/




#include<stdio.h>




int main()
 {
    int x,n,t=1,i,j;
    double num,sum=0.0,r;
    long int deno;


    printf("\n\t\tINPUT:");
    printf("\n\t\t------");
    printf("\n\t\tEnter the value for x:  ");
    scanf("%d",&x);
    printf("\n\t\tEnter the value for n:  ");
    scanf("%d",&n);
    printf("\n\t\tOUTPUT:");
    printf("\n\t\t-------");
    r=x*(3.14/180.0);
    printf("\n\t\tThe radius value for the given x value is:  %lf",r);
    for(i=1;i<=n;i+=2)
     {
       num=1.0;
       deno=1;
       for(j=1;j<=i;j++)
         {
           num=num*r;
           deno=deno*j;
         }
       sum=sum+num/deno*t;
       t=t*-1;
       printf("\n\t\tThe value for sin %d is:  %.11f",x,sum);
     }


    printf("\n\n\n");
    return 0;
  }

[anduril462]

Can you use a MacLaurin series to estimate sin(x) correctly with paper and pencil? If you can't solve a problem, you can't program a computer to do it. Just a few small examples calculated to 4 or 5 terms should be sufficient. Make sure you write out each term, listing the numerator, denominator and "x" term (x**3, x**5, etc). Compare your by-hand calculation to what your program produces at each step (add printfs to print out all necessary value on each loop iteration). Where do you see deviations?

You should also use a more accurate value for pi when converting degrees to radians. Better more accurate than less. It might be best if you simply let the user input the angle in radians to begin with though, and eliminate any source of error from deg->rad conversion.

[Salem]

> int x,n,t=1,i,j;
> double num,sum=0.0,r;
> long int deno;
Having variables like
double xPowerN;
double nFactorial;

would go a long way to clarifying your code purpose, as opposed to a handful of single letter and generic names.