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Polar Graphs

Coordinate geometry is a vast subject that plays a vital role in mathematics. An object or a point is defined through its position. The position is expressed in the space by the means of coordinates. There are various coordinate systems that are used to define the coordinates of an object. These coordinate systems are - Cartesian coordinate system, polar coordinate system, cylindrical coordinate system, spherical coordinate system. Here, we are going to study about polar coordinate system.

Get help with polar coordinates and types of it in this page. The polar coordinate graph is a two dimensional polar coordinate system. This plane is determined by two types:

  • A distance from a fixed point and
  • An angle from a fixed direction.
The fixed point of a polar coordinate system is referred to as pole and the fixed direction of a polar system is referred to as polar axis. The angle from the pole is denoted as polar angle and the distance from the pole is denoted as radius. The polar graph is the function of r and $\theta$; where r is the distance and $\theta$ is referred to the angle. The equation of the polar graph is r = f ($\theta$). Let us understand more about polar coordinates and polar graphs.

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Polar Curves

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The curve is a 3- dimensional space or a plane. This can be classified into various types such as circles, arcs, lines, parabolas etc.

Types of Polar Graphs

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Here is explained the different types of polar graphs with diagrams:

Cardioids:

The shape of the cardioids are heart shape. It is defined as resembles point on a radius(or circle) that rolls around the fixed radius of the same circle.

The two cardioids figures given below,

Horizontal cardioids equation :

`r=a` `+-` `acostheta`

Horizontal cardioids

Vertical cardioids equation :

` r=a` `+-` `asintheta`

Vertical cardioids

Lemniscates:

This curve is usually represented in polar coordinate system and also that resembles a figure eight form.

The equation of lemniscates given below,

` r^2=a^2cos2theta` or

` r^2=a^2sin2theta`


lemniscates

Limacons:

This is similar to cardioid. Cardioid is a special kind of limacons family of related curves.

Limacon equations:

`r = b + a costheta` (horizontal) or

` r = b + a sintheta` (vertical)


limacon

Rose curves :

This graph is a smooth curve that can be arranged symmerically in common center.

We are using sine and cosine equations.

Rose Curves

Spirals:

This curve is endlessly in outward or inward. The spirals can be represented into various types is given below,

Spirals

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