Write a C++ program to compute Sin(x)
CodeGuru Home VC++ / MFC / C++ .NET / C# Visual Basic VB Forums Developer.com
Results 1 to 9 of 9

Thread: Write a C++ program to compute Sin(x)

  1. #1
    Join Date
    Nov 2012
    Posts
    6

    Write a C++ program to compute Sin(x)

    Hi. I'm having problem writing this program as my assignment. I've spent hours on this but still i can't get the right answer.

    Here is the question:
    Write a C++ program to compute Sin(x) where

    x x^3 x^5 x^7 x^9 x^n
    sin (x) = ----- ─ ---- + ---- ─ ---- + ----- ─ . ------
    1! 3! 5! 7! 9! n!

    Your program should accept two values from the user (the angle x and the value of n) and then should compute and print the value of sin(x).

    To make the program, do following tasks.

    Write two functions, i.e. function to calculate factorial and function to calculate power having following prototypes.
    double Factorial (int n); //Factorial function prototype
    double Power(double x, int y); //Power function prototype
    Use these functions in your main function to compute the series.

    Till now, I've written the following program but I am not able to get the right answer.

    #include <iostream>
    using namespace std;

    double fact (int f); //declaration of factorial function

    double power(double x, int y); //declaration of power function


    int main()
    {
    int x=0; //value of x in the series
    float sum_pos = 0;
    float sum_neg=0;
    float t_sum=0;

    cout << "Enter the value of x: " << endl;
    cin >> x;

    for (int i=1; i<=1000; i+=4)
    {
    sum_pos = sum_pos + (power (x,i) / fact (i));
    }

    for (int i=3; i<=1000; i+=4)
    {
    sum_neg = sum_neg + (power (x,i) / fact (i));
    }

    t_sum = sum_pos - sum_neg;

    cout << "Sin of " << x << " = " << t_sum << endl;

    return 0;
    }

    //Function for Factorial
    double fact (int x)
    {
    double f=1;

    if (x==0)
    {
    return f;
    }

    else
    for (int i=1; i<=x; i++)
    {
    f=f*i;
    }

    return f;
    }

    //Function for Power
    double power (double x, int y)
    {
    int p=1;

    for (int i=1; i<=y; i++)
    p=p*x;

    return p;
    }

    I have to submit it this weekend. So please help me what am i doing wrong??

  2. #2
    Join Date
    Nov 2012
    Posts
    6

    Re: Write a C++ program to compute Sin(x)

    the series is:

    x x^3 x^5 x^7 x^9 x^n
    sin (x) = ----- ─ ---- + ---- ─ ---- + ----- ─ …………. ------
    1! 3! 5! 7! 9! n!

  3. #3
    VictorN's Avatar
    VictorN is online now Super Moderator Power Poster
    Join Date
    Jan 2003
    Location
    Wallisellen (ZH), Switzerland
    Posts
    17,358

    Re: Write a C++ program to compute Sin(x)

    You have to use Code tags to properly format the posted code and formulas.
    See Announcement: Before you post....
    Victor Nijegorodov

  4. #4
    Join Date
    Aug 2000
    Location
    West Virginia
    Posts
    7,564

    Re: Write a C++ program to compute Sin(x)

    1) you have "x" declared as int instead of double in main()
    and the "p" variable declared as int instead of double in power()

    2) You should use "double" instead of "float"

    3) fyi : "x" is in radians, not degrees

    4) There is no need to go all the way to "i=1000" ..., write a small program
    that just prints out fact(i), you will see a problem.

    5) The equation that you are using is best suited for x values near zero.
    You can use trig identities to make the value of "x" smaller before
    calculating the sin (example : sin(x + 2*pi) = sin(x)... So there is no need
    to use any value greater than 2*pi. And actually, that range can be reduced
    significantly using other trig identities).
    Last edited by Philip Nicoletti; November 8th, 2012 at 07:06 AM.

  5. #5
    Join Date
    Apr 2000
    Location
    Belgium (Europe)
    Posts
    3,845

    Re: Write a C++ program to compute Sin(x)

    Also note that the above formula calculates sin(x) where x is in radians, not in degrees.
    if you are trying to manually check if a certain value matches what you get on a calculator, then you need to set your calculator to radians.

    a 30 angle would be Pi/6 radians so your function should be returning sin( pi/6 ) or sin( 0.5235987755983 ) as being (more or less) equal to 0.5

    But as philip posted above, your real problem is in trying to make your program "too good". You're causing a problem by making the loop go to 1000.

  6. #6
    Join Date
    Nov 2012
    Posts
    6

    Re: Write a C++ program to compute Sin(x)

    How many times should I make the loop go on if not 1000??

  7. #7
    Join Date
    Aug 2000
    Location
    West Virginia
    Posts
    7,564

    Re: Write a C++ program to compute Sin(x)

    What type of course is this for ? If a numerical analysis course, the
    error for truncated a Taylo series should be given in the text book.

    At any rate ... you ahve an alternating series that is monotomically
    decreasing, the absolute value of the error when stopping the series
    at a certain term is less than or equal to the first dropped term.

    In pratical terms, choose a tolerance (say 10e-6), and stop iterating
    when the term that you calculate is less than or equal to the tolerance.

  8. #8
    Join Date
    Apr 2000
    Location
    Belgium (Europe)
    Posts
    3,845

    Re: Write a C++ program to compute Sin(x)

    Computers deal with numerical types that have operational constraints.

    A double for instance has an upper bound of the largest number it can contain. This upper bound has a define DBL_MAX which is 1.797E+308. If you are making calculations and any (intermediate) value you calculate exceeds the operational constraints you get overflow (or underflow, or one of several other undesired effects). Once this happens, all bets are off concerning the end result, you could get results that make absolutely no sense at all.

    Dealing with floating point numbers correctly posses additional problems. Floating point values are NOT accurate values, they are approximations. Each value has a slight error to it. Depending on how you deal with the numbers you can continuously accumulate more error into your intermediate results (or worse, scale/multiply it). This too can throw your results off whack.

    For taylor series specifically there are ways to calculate how much iterations you need to achieve the desired precision. And when dealing with floating point, there are ways to reduce error accumulation. And there are ways to figure out if floating point error would exceed the desired precision meaning calculation isn't possible with the current algorithm or the used floating point type.

    I doubt all the above is relevant for you, if this is a simple course, then see if you have an iteration value in the text book. If that is not there, you will need to to find an iteration in such a way that none of the intermediates overflow. In short, find an i where power(i) and fact(i) never exceed 1.797E+308 (to avoid precision loss, you probably do NOT want to not the highest possible i that meets this requirement, but want an i that's a bit lower)

  9. #9
    Join Date
    Jan 2009
    Posts
    596

    Re: Write a C++ program to compute Sin(x)

    Quote Originally Posted by weirdom3 View Post
    How many times should I make the loop go on if not 1000??
    Rule 1: Always read the problem statement carefully. As you said in your first post:

    Quote Originally Posted by weirdom3 View Post
    Here is the question:
    Write a C++ program to compute Sin(x) where

    x x^3 x^5 x^7 x^9 x^n
    sin (x) = ----- ─ ---- + ---- ─ ---- + ----- ─ . ------
    1! 3! 5! 7! 9! n!

    Your program should accept two values from the user (the angle x and the value of n) and then should compute and print the value of sin(x).
    See the bits in red? You are only asking for x, not n

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  


Azure Activities Information Page

Windows Mobile Development Center


Click Here to Expand Forum to Full Width

This is a CodeGuru survey question.


Featured


HTML5 Development Center