# C Program to Convert Polar Coordinate to Cartesian Coordinates

In mathematics, a Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numeric points.

Cartesian Coordinates is represented by (x,y).

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point known as radius and an angle from a reference direction known as theta or simply angle.

Polar Coordinates system is represented by (r,θ).

## Formula to Convert Polar Coordinate to Cartesian Coordinate

To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) :
x = r × cos( θ )
y = r × sin( θ )

## Polar to Cartesian C Program

``````
#include<stdio.h>
#include<conio.h>
#include<math.h>

#define PI 3.141592

int main()
{
float x, y, r, theta;
clrscr();
printf("Enter radius of polar coordinate (r): ");
scanf("%f", &r);
printf("Enter angle of polar coordinate in degree (theta): ");
scanf("%f", &theta);

/* Converting theta from degree to radian */
theta = theta * PI/180.0;

/* Calculating cartesian coordinate x */
x = r * cos(theta);

/* Calculating cartesian coordinate y */
y = r * sin(theta);

printf("Cartesian coordinates is: (%0.3f, %0.3f)", x, y);
getch();
return(0);
}
``````

Output of the above program :

```Enter radius of polar coordinate (r): 1.4142 ↲
Enter angle of polar coordinate in degree (theta): 45 ↲
Cartesian coordinates is: (1.000, 1.000)

Note: ↲ indicates ENTER is pressed.
```