Sine is a trigonometric angle of a right-angled triangle For a better understanding of this sinx C program example, we always recommend you to learn the basic topics of C programming listed below:

Here in this C program, we will find out the value of **sine x** up to the given accuracy. **Sine** is the trigonometric function of an angle of a right triangle. For an angle, sine value is defined as the ratio of length and side opposite that angle to the hypotenuse. [ means the longest side of the triangle ].

Normally all trigonometric functions are defined as the ratio of sides of the triangle, which have an angle too. The sine values for the defined angles are** sine 0 = 0**, **sine 90 = 1**, **sine 30 = .5** etc.

Here this c program, we find out the value of **sine x** up to the given accuracy. For that, firstly, we are converting the given **degrees** to **radians**. We are using a `do-while`

loop and use the steps given below.

` ````
den = 2*n*(2*n+1);
term = -term * x * x / den;
sinx = sinx + term;
n = n + 1;
```

In this C program, after importing the header files, we are accepting the value of **x** in degrees. We save that value in a variable, and now to apply the formula, we need to convert the degree to radians using the formula **'pi / 180'**. We get the needed accuracy from the user, and we save the value of the angle in radian in a variable '**x**,' and we copy the '**x**' to another variable and assign that to the **sin(x)**. Now open a `do-while`

loop to check calculate value using **den =2*n*(2*n+1)**, then using '**den**' we calculate the **term = -term * x * x / den;** .And **sinx - sinx = sinx + term;** we do the loop until the condition **acc <= fabs(sinval - sinx)** will be true. Finally printing the value of **sinx** as a result.

**STEP 1:** Import the Header files into the C program to use the built-in functions.

**STEP 2:** Accept the value of the angle in Degree using `printf`

and `scanf`

and save that in the variable.

**STEP 3:** Initialize and Define the variable for the C program.

**STEP 4:** Save the value of the angle in Degree into a variable and convert the Angle to Radians using **'pi / 180**'.

**STEP 5:** Assign the value of **sin(x)** to a variable using **sinval**.

**STEP 6:** Accept the accuracy value from the user using `printf`

and `scanf`

and save that to a variable.

**STEP 7:** Save the value of **term =x** and **sinx = term** and **n = 1.**

**STEP 8**: Open a '`do while`

**'** loop condition till the condition meets (**acc <= fabs(sinval - sinx)**).

**STEP 9: **Calculate the value of '**den**' by using the formula **den = 2*n*(2*n+1)**.

**STEP 10:** Calculate the Term Value using the formula -**term * x * x / den**. Using that, calculate the value of **sinx** by **sinx + term** and increment the **n** by **1**.

**STEP 11:** Print the result of the Sine series using the `printf`

and using the C programming language.

` ````
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
void main()
{
int n, x1;
float acc, term, den, x, sinx=0, sinval; /* declares acc, term, den, sinx, sinval as float */
printf("Enter the value of x (in degrees)\n"); /* gets the value of x in degrees */
scanf("%f",&x);
x1 = x;
x = x*(3.142/180.0); /* Converting degrees to radians*/
sinval = sin(x);
printf("Enter the accuracy for the result\n"); /* receives value of accuracy */
scanf("%f", & acc);
term = x;
sinx = term;
n = 1;
/* enters do while loop and use the formula to find den */
do
{
den = 2*n*(2*n+1);
term = -term * x * x / den;
sinx = sinx + term;
n = n + 1;
} while(acc <= fabs(sinval - sinx)); /* while condition checking */
printf("Sum of the sine series = %f\n", sinx);
printf("Using Library function sin(%d) = %f\n", x1,sin(x)); /* prints the value of sinx */
}
```

Enter the value of x (in degrees) 30 Enter the accuracy for the result 0.000001 Sum of the sine series = 0.500059 Using Library function sin(30) = 0.500059 RUN 2 Enter the value of x (in degrees) 45 Enter the accuracy for the result 0.0001 Sum of the sine series = 0.707215 Using Library function sin(45) = 0.707179