## 28 Replies - 21489 Views - Last Post: 25 July 2010 - 11:34 AM

### #1

# taylor series in c++

Posted 09 July 2010 - 04:11 AM

please see this picture

now my question if x = 2.3145

Q1 how much will be cosine, sine and tangent?

Q2 i tried to ues the above fourmlaes to find the value of x but it's not correct,so could you please show me how can i cuclate it?

please note that i'm really poor in math

then after i know the answers i can do it in c++

waiting for you

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**Replies To:** taylor series in c++

### #2

## Re: taylor series in c++

Posted 09 July 2010 - 04:36 AM

but what is the fourmlas for?? the fourmlas make me confuse

### #3

## Re: taylor series in c++

Posted 09 July 2010 - 07:14 AM

2. Then check out our snippet section

In short, The Taylor Series is an approximation of the trig function(s).

### #4

## Re: taylor series in c++

Posted 09 July 2010 - 08:28 AM

for the second link it's ok but my question

Quote

but what is the fourmlas for?? the fourmlas make me confuse

### #5

## Re: taylor series in c++

Posted 09 July 2010 - 08:37 AM

If you look at the full series, you get an infinite sum (so getting a precise value isn't possible). So I would imagine that your calculator does something along the lines of evaluating the part of the taylor series until a reasonable approximation is made.

See Here: http://en.wikipedia....ies_definitions

L.N

### #6

## Re: taylor series in c++

Posted 09 July 2010 - 09:17 AM

here is my way whan i want to use the fourma for sin(x)

lt say x = 1

sin(1) = 1 - 1^3/3*2*1 + 1^5/5*4*3*2*1 and so on, but this way is not correct

so i;m lookeing for the correct way ( x = 1)

so can anybody show me?

one more Q

what is the relationship between the forumlas above and this forumla

### #7

## Re: taylor series in c++

Posted 09 July 2010 - 09:31 AM

This post has been edited by **xtreampb**: 09 July 2010 - 09:33 AM

### #8

## Re: taylor series in c++

Posted 09 July 2010 - 09:31 AM

muti post

This post has been edited by **xtreampb**: 09 July 2010 - 09:34 AM

### #9

## Re: taylor series in c++

Posted 09 July 2010 - 09:32 AM

L.N

This post has been edited by **LivingNightmare**: 09 July 2010 - 09:34 AM

### #10

## Re: taylor series in c++

Posted 09 July 2010 - 11:18 AM

but my way is not correct

can you please try and show me here?

waiting for you

### #11

## Re: taylor series in c++

Posted 09 July 2010 - 11:23 AM

To evaluate sin(pi) you would calculate sin(pi) = pi - (pi^3)/3! + (pi^5)/5! - (pi^7)/7! + (pi^9)/9! ... and you would keep going until you have the desired precision. However, in this case sin(pi) is simply equal to 0. Also, note that for a positive integer N, N! = N*(N-1)*(N-2)*...*2*1. So 5! would be equal to 5*4*3*2*1 = 120.

L.N

### #12

## Re: taylor series in c++

Posted 09 July 2010 - 11:47 AM

#include <iostream> #include <cmath> using namespace std; double factorial(double num) { double ret = 1; while(num > 0) { ret *= num; num--; } return ret; } double MySine(double rad, int n) { double value = 0; for(int i = 0; i < n; i++) { value += pow(-1.0, i) / factorial((2*i) + 1) * pow(rad, ((2*i) + 1)); } return value; } int main() { double p = 3.1415926; cout<<"Sine of pi is: " <<MySine(p, 12) <<endl; return 0; }

The factorial function simply evaluates N! - Then MySine approximates Sin(rad) by using it's taylor series expansion.

L.N

### #13

## Re: taylor series in c++

Posted 09 July 2010 - 02:25 PM

and i find the correct way

first i have to do this

3!=6

5!=120

7!=5040

9!=362880

then

sin(1)=1-1/6+1/120-1/5040+1/362880

### #14

## Re: taylor series in c++

Posted 09 July 2010 - 02:43 PM

L.N

This post has been edited by **LivingNightmare**: 09 July 2010 - 02:43 PM

### #15 Guest_empror9*

## Re: taylor series in c++

Posted 24 July 2010 - 04:42 PM

this is my function to approximate sin(x)

float sin(float x) { float result = x; int limit = 15; int sign = -1; for(int i=3 ; i<limit ; i+=2,sign=-sign) result += sign*result*(x*x)/(i*(i-1)); return result; }

and this to approximate cos(x)

float cos(float x) { float result = 1; int limit = 15; int sign = -1; for(int i=2 ; i<limit ; i+=2,sign=-sign) result += sign*result*(x*x)/(i*(i-1)); return result; }

but the answer is not clear in some cases and in other cases it displays wrong answers

try to input 1.5707963

cos should equals to 0.0000000

but my function shows -0.263853, so the answer is not that good

waiting for you