Polar Coordinate System

The polar coordinate system is an angle that defines a two-dimensional coordinate system consisting of points and a distance from a central point called the pole in mathematics (equivalent to the origin in the more familiar Cartesian coordinate system). Several subjects, including mathematics, physics, engineering, navigation, and robotics, utilise the polar coordinate system. It’s beneficial when the relationship between two points is best stated in terms of angles or distance; thus, a relationship could only be discovered using trigonometric formulae in the Cartesian coordinate system. A polar equation seems to be the simplest means of representation for several types of curves; for others, it is the only option.

Polar Coordinate System

The polar coordinate system seems to be a two-dimensional coordinate system. A distance from a reference point and an angle from the reference direction identify each point on a plane. The pole seems to be the reference point (analogous to a Cartesian coordinate system). Also, the polar axis is the ray extending from the pole in the reference direction. The radial coordinate, radial distance, or simply radius, is just the distance from the pole, while the angular coordinate, polar angle or azimuth, is the angle. In polar notation, angles are often written in degrees or radians (2 rad equals 360°).

Polar coordinates were best used in situations where the studied phenomenon is inextricably linked to the direction and length of a plane’s centre point, including spirals. Using polar coordinates, it is generally more straightforward to model planar physical systems with bodies moving about a centre point or phenomena emerging from a central point. The cylindrical and spherical coordinate systems are two techniques to expand the polar coordinate system to three dimensions.

Cartesian and Polar Coordinates

Coordinates are being used to represent the position of a point in space in a unique way which implies that we have two dimensions like a piece of paper: height and width (no depth). Draw perpendicular lines to one another to create a Cartesian coordinate system. As a result, the origin is the place wherever they meet. The distance between the point in space and the two lines denoted by the x-axis and y-axis is coordinate. All vertical lines are included in the polar system’s origin. 

A place known as a pole is the source of a polar system. An arbitrary ray will be chosen as the polar axis starting from this point. The rectangular to polar coordinates calculator must first discover then draw a connecting line before calculating the polar coordinates of a given point. Therefore, the length of the line r and the angle between the polar axes are the coordinates of these places. Our polar coordinates calculator will convert between Cartesian or polar coordinates.

How does the Polar Coordinate System Calculator Work?

Following these methods, an online polar coordinate calculator would convert polar coordinates to a rectangle and, conversely:

Input: 

• First, choose a conversion type, including Cartesian to polar or Cartesian.

• Substitute the values in the fields that are connected now.

• To see the conversion, press the calculate button.

Output:

• The Polar Coordinates Calculator performs conversions based on the degree or radian values entered.

• The polar to Cartesian equation calculator additionally shows step-by-step coordinate calculations.

Relative Polar Coordinate System

The last point entered determines relative coordinates. If you know the location of a point about the previous point, utilise relative coordinates.

To express relative coordinates, use a @ symbol before the coordinate values. For instance, entering @145 specifies a location 1 unit further from the previous point at a 45-degree angle from the X-axis.

Two lines drawn using relative polar coordinates are shown in the following scenario. The line in each figure starts where the primary point is labelled.

Command: line

From point: @3<45

To point: @5<285

Conclusion

For the transition between polar and rectangular coordinates, use this Polar Coordinates Calculator. A polar coordinate system is a two-dimensional coordinate system. A distance from a reference point and an angle from a reference direction have been used to identify each point on just a plane. In polar notation, angles are often written in degrees or radians (2 rad equals 360°). I hope now you understand all about the polar coordinate system with a calculator and the relative polar coordinate system in detail. For better understanding, you must go through the topic thoroughly so that it will clear all your doubts.