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Graphing Polar Equations

In this article we are going to discuss about Graphs of Polar-Coordinate Equations. Before we going to to draw the graph of Polar-coordinate Equation, we have to know about Polar coordinate, Polar graph and Polar equation.

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Polar Coordinate

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Polar coordinate is define as several ways, But one of them or easier one is describe below.In this way we are representing distance and direction. Distance from a particular point known as pole and Direction in a fixed angle. Suppose the distance is 5 unit and from fixed point or pole and in the direction of 60 degrees, so it is represented as (5, 600 ).

Figure of Polar coordinate

Here O point is known as pole and the line OB is is the axis and the distance between two points O and A. is known as radical distance, An angle 60 degrees is the direction from line or axis , it is generally represented as degrees or radians.In two dimension polar coordinate the distance between two points and the direction from the axis. Distance are represented as r and the direction from the axis in anticlockwise direction is represented as `theta` , and the polar coordinate is represented as (r, `theta` ).

polar coordinates

Polar Graph

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The polar coordinate system is a two 2-D the polar coordinate graph. This plane is determined by two types:

  • A distance of two points and
  • An direction from the axis or line

In two dimension polar coordinate the distance between two points and the direction from the axis. Distance are represented as r and the direction from the axis in anticlockwise direction is represented as `theta` ,

There are five different types of polar graph in the polar coordinate system and these are mentioned below namely:

  • Cardioids Polar Graph
  • Lemniscates Polar Graph
  • Limacons Polar Graph
  • Spirals Polar Graph
  • Rose curves Polar Graph

Polar Equations

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The equation of terms written in terms of the polar coordinate system theta (`theta`) and radius (r). For example equation of polar equation is given below,

r = sin2 `theta` and

r = cos2`theta`

So far we have learn how to graph a point with polar coordinates (r, ?). Now lets see graphing polar equations. We know the polar coordinate system is similar to rectangular coordinate system. In a polar coordinate field, there will be a series of circles extending out from the pole(origin in Cartesian system) and five different lines passing through the pole to represent the angles.

We have value for every angle in trigonometric functions, below is the representation of polar co ordinate system and its angular values.

Polar co ordinate and polar degree

Aids in Graphing Polar-coordinate Equations

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The traditional aid in graphing Polar-Coordinate equation is by using the table values and rules of symmetry. There are number of aids of graphing polar co ordinate equation. Let us see symmetry property of any graph.

The traditional aid in graphing Polar-Coordinate equation is by using the table values and rules of symmetry. There are number of aids of graphing polar co ordinate equation. Let us see symmetry property of any graph.


More topics in Graphing Polar Equations
Polar Equation of a Circle
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