The program to compute cosine series is based on mathematical concept of sequences and series – particularly power series.

This program is written using Dev-C++ compiler, but you can use any standard C compiler to compile and run the program. This program is intended for beginners as well as intermediate learners of C programming.

To help you learn, we have following sections – problem definition, flowchart, program source code and verified output of the program.

### Problem Definition

Cosine series is a power series known as the Maclaurin expansion of **Cos(x)** where **x** is a real number value. Given the value of x, the series will converge and give a finite value ( radius of convergence) for the series.

cos(x) = ^{∞}∑_{k=0}= (-1)^{k}x^{2k}/(2k)! = 1 – x^{2}/2! + x^{4}/4! – x^{6}/6! …

We won’t be discussing, how terms of the series are generated because that would be topic for another post. The Maclaurin expansion for cos(x) is for x =0, however, it is true for all real values of x.

In other words, it is same as finding the value of trigonometric ratio of **cos θ**, the cosine series will give you a better approximate value of **cos θ**.

### Flowchart

### Program Code

`/* Program to compute cosine series */ /* cos(x) = 1-x^2/2!+x^4/4!+x^6/6!+...+x^n/n! */ #include <stdio.h> #include <stdlib.h> #include <math.h> main() { float x, t, sum; int d; int i, n=20; /* Read the Input x value in degrees */ printf ("Input X Value (in degrees) :"); scanf ("%f", &x); d= x; /*converting x to radians */ x=x*3.1412/180; t=1; sum=1; for (i=1; i<n+1; i++) { t=t*pow ((double) (-1), (double) (2*i-1))*x*x/ (2*i*(2*i-1)); sum=sum+t; } /* Print the Results */ for (i =0; i<35; i++) printf ("_"); printf ("\n\n"); printf ("COS (%d) =%7.3f\n\n", (int) d, sum); for (i =0; i<35; i++) printf ("_"); printf ("\n\n"); system ("PAUSE"); return 0; }`

### Output

The output of the program is given below.