Jonn Ralge Yuvallos - 15 days ago 12

C Question

I've been following the guide my prof gave us, but I just can't find where I went wrong. I've also been going through some other questions about implementing the Taylor Series in C.

Just assume that RaiseTo(raise a number to the power of x) is there.

`double factorial (int n)`

{

int fact = 1,

flag;

for (flag = 1; flag <= n; flag++)

{

fact *= flag;

}

return flag;

}

double sine (double rad)

{

int flag_2,

plusOrMinus2 = 0; //1 for plus, 0 for minus

double sin,

val2 = rad,

radRaisedToX2,

terms;

terms = NUMBER_OF_TERMS; //10 terms

for (flag_2 = 1; flag_2 <= 2 * terms; flag_2 += 2)

{

radRaisedToX2 = RaiseTo(rad, flag_2);

if (plusOrMinus2 == 0)

{

val2 -= radRaisedToX2/factorial(flag_2);

plusOrMinus2++; //Add the next number

}

else

{

val2 += radRaisedToX2/factorial(flag_2);

plusOrMinus2--; //Subtract the next number

}

}

sin = val2;

return sin;

}

int main()

{

int degree;

scanf("%d", °ree);

double rad, cosx, sinx;

rad = degree * PI / 180.00;

//cosx = cosine (rad);

sinx = sine (rad);

printf("%lf \n%lf", rad, sinx);

}

So during the loop, I get the rad^x, divide it by the factorial of the odd number series starting from 1, then add or subtract it depending on what's needed, but when I run the program, I get outputs way above one, and we all know that the limits of sin(x) are 1 and -1, I'd really like to know where I went wrong so I could improve, sorry if it's a pretty bad question.

Answer

Anything over `12!`

is larger than can fit into a 32-bit `int`

, so such values will overflow and therefore won't return what you expect.

Instead of computing the full factorial each time, take a look at each term in the sequence relative to the previous one. For any given term, the next one is `-((x*x)/(flag_2*(flag_2-1))`

times the previous one. So start with a term of `x`

, then multiply by that factor for each successive term.

There's also a trick to calculating the result to the precision of a `double`

without knowing how many terms you need. I'll leave that as an exercise to the reader.