I need help with Taylor Series
Part A:
Scan the angle in degrees x_deg. Express this angle in
radians by using x=PI*x_deg/180, and calculate Y=cos^2(x)
by using the math.h library of functions (pow() and cos()
functions). Compare the so calculated value of Y=cos^2(x)
with the approximate value y obtained by using n_term
terms of the Taylor series
cos^2(x)=0.5*(1 +Sum[(1)^n (2*x)^(2n)/(2n)!]),
where n goes from 0 to n_term. Print the relative error
100*(Yy)/Y.
Scan an integer value of n_term. Evaluate (2n)! by an embedded
forloop statement. Use two do/while statements to continue
the calculations for different n_term and different x_deg. For
example, use flag=1 to continue calculations for different n_term
within the inner do/while loop, and flag=0 to exit that loop.
Use Flag=1 to continue calculations for different x_deg
within the outer do/while loop, and Flag=0 to exit that loop
and go to Part B. (Recall that 0!=1).
This is my program:
#include <stdio.h>
#include <math.h>
#define PI 3.141592654
main()
{
int n_terms, n=0;
double angle_deg, angle_rad, csa, csa2, taylor, sum;
printf("\n\nPar t A:\nCalculation of True and Approximate Values of cos^2(x)\n\n");
printf("Enter x_deg: \n");
scanf("%lf", &angle_deg);
angle_rad = angle_deg * (PI/180.);
csa = cos(angle_rad);
csa2 = pow(csa, 2.);
printf("True value of cos^2(x) = %f\n\n", csa2);
printf("n_term approximation of cos^2(x)\n\n");
printf("Enter number of terms:\n");
scanf("%d", &n_terms);
printf("\n%d term approximation\n ", n_terms);
}
so far everything shows up correctly. I'm just stuck on how to use the for loop to calculate the taylor series.
12 39201 Banfa 9,065
Recognized Expert Moderator Expert
The pseudo code to calculate the value of any series goes something like this 
INITIALISE SERIES VALUE


FOR EACH TERM IN THE SERIES

SERIES VALUE = SERIES VALUE + VALUE OF TERM

END FOR


OUTPUT SERIES VALUE

sorry, i'm new to programming
could you give like a simple example of how to do it? how many double / float values would i need to define?
Banfa 9,065
Recognized Expert Moderator Expert
A minimum of 1 double value to hold the total and 2 integer values, 1 to hold the current term number and 1 to hold the number of terms to evaluate. You may need more for complex terms or to make the calculation more readable.
so taking ** to mean to the power of (e.g. 3 ** 2 = 9) to evaluate the series
1 / (2**0) + 1 / (2**1) + 1 / (2**2) + 1 / (2**3) + 1 / (2**4) + ... + 1 / (2**n)
i.e. the some of recipricals of the powers of 2 (this tends to the value 2)
the code could look something like 
#include <stdio.h> /* For the pow function */

#include <math.h> /* For the pow function */


int main()

{

double value;

int term;

int number_of_terms = 10; /* Note I have arbitarily chose this value for this case */


value = 0.0; /* Initialise series value */


/* For each term required */

for( term=0; term<number_of_terms; term++)

{

value += 1.0 / pow(2.0, term); /* Add the value of this term to the total */

}


printf( "The sum of the recipricol of the powers of 2 to %d terms is %f\n",

number_of_terms,

value);

return 0;

}
okay thanks
i'll see if that works and update if it does or not =]
okay, i tried to do what you said. this is the code i came up with.
#include <stdio.h>
#include <math.h>
#define PI 3.141592654
main()
{
int n_terms, n=0;
double angle_deg, angle_rad, csa, csa2, value;
printf("\n\nPar t A:\nCalculation of True and Approximate Values of cos^2(x)\n\n"
);
printf("Enter x_deg: \n");
scanf("%lf", &angle_deg);
angle_rad = angle_deg * (PI/180.);
csa = cos(angle_rad);
csa2 = pow(csa, 2.);
printf("True value of cos^2(x) = %f\n\n", csa2);
printf("n_term approximation of cos^2(x)\n\n");
printf("Enter number of terms:\n");
scanf("%d", &n_terms);
printf("\n%d term approximation\n ", n_terms);
for(n=0; n<n_terms; n++){
value += 0.5 * 1 + (pow(1.0, n) * pow((2 * angle_rad), (2 * n)) / (2 * n));
}
printf("cos^2(x ) = %g", value);
}
is there a definition in C programming that lets me do factorials? because when i defined the value...i need the last (2 * n) to be (2 * n)!.
thanks
This is my program so far. I got the factorial to work.
#include <stdio.h>
#include <math.h>
#define PI 3.141592654
main()
{
int n_terms, n=0;
double angle_deg, angle_rad, csa, csa2, value, sum, factorial;
printf("\n\nPar t A:\nCalculation of True and Approximate Values of cos^2(x)\n\n");
printf("Enter x_deg: \n");
scanf("%lf", &angle_deg);
angle_rad = angle_deg * (PI/180.);
csa = cos(angle_rad);
csa2 = pow(csa, 2.);
printf("True value of cos^2(x) = %f\n\n", csa2);
printf("n_term approximation of cos^2(x)\n\n");
printf("Enter number of terms:\n");
scanf("%d", &n_terms);
printf("\n%d term approximation\n ", n_terms);
for(n=0; n<n_terms; n++){
value = 0.5 * (1 + sum);
sum += (pow(1.0, n_terms) * (pow((2. * angle_rad), (2. * n_terms))/ factorial));
factorial += (2 * (n_terms  n));
}
printf("cos^2(x ) = %g\n", value);
}
however, the value for the taylor series will not come out correctly. anyone have any suggestions. this is what the taylor series should be.
cos^2(x)=0.5*(1 +Sum[(1)^n (2*x)^(2n)/(2n)!])
Banfa 9,065
Recognized Expert Moderator Expert
You never initialise the value factorial
but what if there is no math.h
can you still make a program converting the sine of a number using taylor series?
how? pls help thnx..
Banfa 9,065
Recognized Expert Moderator Expert
but what if there is no math.h
can you still make a program converting the sine of a number using taylor series?
how? pls help thnx..
Why would there be no math.h?
Sign in to post your reply or Sign up for a free account.
Similar topics 
by: Dick Moores 
last post by:
I need to figure out how to compute pi to base 12, to as many digits as
possible. I found this reference,
<http://mathworld.wolfram.com/Base.html>, but I really don't understand
it well enough. Could someone show me how to do what I need?
Thanks,
Dick Moores
rdm@rcblue.com

by: oz 
last post by:
Hi,
Where can i find code examples of connecting with MQ from VB.net(not using
msmq bridge)
BR
Oz

Outgoing mail is certified Virus Free.

by: chb1980 
last post by:
this is a question..about Taylor series...
1) Find the Taylor series approximation of order 2 (n=2) for the funtion f(x,y)=sin(xy) about (x。,y。)=(π/4,π/4) using this approximation , compute the function value at x=0.77 and y=0.80
could you handle it ..?

by: chb1980 
last post by:
this is a question..about Taylor series...
1) Find the Taylor series approximation of order 2 (n=2) for the funtion f(x,y)=sin(xy) about (x。,y。)=(π/4,π/4) using this approximation , compute the function value at x=0.77 and y=0.80
could you handle it ..?

by: mia023 
last post by:
Hi i just want to ask if i want to write a java program that compute sin x and cos x using Taylor series. I don't know the logic about how to write this program and how to get Taylor series through programming
 
by: ninita 
last post by:
Hi everybody!
Does anyone know how to program in java to put the tayor series??
I really need help!

by: pancholijaymin 
last post by:
can i get the solution immediately for the cpp program onthe taylor series which has prototype as follows:
double getTaylorSeries(double xValue, int maxTerm):
Where, the parameter xValue represents the value of x and maxTerm is the maximum limit of the terms

by: arperidot 
last post by:
hey guys, the question asks to
Scan the angle in degrees using x=PI*x_deg/180 and calculate Y=sin^2(x).
Calculate sin^2(x) approximately by using n terms (n>0) the Taylor series
sin(x)=Sum (k goes from 0 to n1)
Scan an integer value of n. Evaluate (2k+1)! by an embedded forloo statement. Use two do/while statements to continue the calculations for different n and different x_deg.
Calculate the error between the Y value and the...

by: Ben Stone 
last post by:
I am trying to write C code for sin(x) using the first 5 terms of the taylor series. I am new to programming and am not allowed to use loops. I don't have much yet, but what I have so far is:
/* solution to Taylor Series approximation of sin(x) */
#include <stdio.h>
#define PI 3.1416f
int main ()
{
float x_deg;

by: marktang 
last post by:
ONU (Optical Network Unit) is one of the key components for providing highspeed Internet services. Its primary function is to act as an endpoint device located at the user's premises. However, people are often confused as to whether an ONU can Work As a Router. In this blog post, we’ll explore What is ONU, What Is Router, ONU & Router’s main usage, and What is the difference between ONU and Router. Let’s take a closer look !
Part I. Meaning of...

by: Hystou 
last post by:
Most computers default to English, but sometimes we require a different language, especially when relocating. Forgot to request a specific language before your computer shipped? No problem! You can effortlessly switch the default language on Windows 10 without reinstalling. I'll walk you through it.
First, let's disable language synchronization. With a Microsoft account, language settings sync across devices. To prevent any complications,...
 
by: Oralloy 
last post by:
Hello folks,
I am unable to find appropriate documentation on the type promotion of bitfields when using the generalised comparison operator "<=>".
The problem is that using the GNU compilers, it seems that the internal comparison operator "<=>" tries to promote arguments from unsigned to signed.
This is as boiled down as I can make it.
Here is my compilation command:
g++12 std=c++20 Wnarrowing bit_field.cpp
Here is the code in...

by: jinu1996 
last post by:
In today's digital age, having a compelling online presence is paramount for businesses aiming to thrive in a competitive landscape. At the heart of this digital strategy lies an intricately woven tapestry of website design and digital marketing. It's not merely about having a website; it's about crafting an immersive digital experience that captivates audiences and drives business growth.
The Art of Business Website Design
Your website is...

by: Hystou 
last post by:
Overview:
Windows 11 and 10 have less user interface control over operating system update behaviour than previous versions of Windows. In Windows 11 and 10, there is no way to turn off the Windows Update option using the Control Panel or Settings app; it automatically checks for updates and installs any it finds, whether you like it or not. For most users, this new feature is actually very convenient. If you want to control the update process,...

by: agi2029 
last post by:
Let's talk about the concept of autonomous AI software engineers and nocode agents. These AIs are designed to manage the entire lifecycle of a software development project—planning, coding, testing, and deployment—without human intervention. Imagine an AI that can take a project description, break it down, write the code, debug it, and then launch it, all on its own....
Now, this would greatly impact the work of software developers. The idea...

by: conductexam 
last post by:
I have .net C# application in which I am extracting data from word file and save it in database particularly. To store word all data as it is I am converting the whole word file firstly in HTML and then checking html paragraph one by one.
At the time of converting from word file to html my equations which are in the word document file was convert into image.
Globals.ThisAddIn.Application.ActiveDocument.Select();...

by: 6302768590 
last post by:
Hai team
i want code for transfer the data from one system to another through IP address by using C# our system has to for every 5mins then we have to update the data what the data is updated we have to send another system
 
by: muto222 
last post by:
How can i add a mobile payment intergratation into php mysql website.
 