Calculus

 Polar coordinate system

Two-dimensional coordinate system. 

Each point is defined by an angle and a distance. 

Cartesian coordinate system is related to polar coordinate system by the application of trigonometry. 

Two polar coordinates are Polar angle (angular coordinate or azimuth angle) and polar distance (radial coordinate). 

Pole in polar coordinate system is equivalent to the origin in cartesian system. 

The zero ray corresponds to polar axis which is like the x-axis in Cartesian coordinate. All angles are measured from the polar axis. 

r>=0 and theta lies between [0, 360] or [-180, 180]
 
arctan means tan inverse

Polar equation: It expresses an algebraic curve in polar coordinates.

Different forms of symmetry can be deduced:

Examples:
 r(-t)= r(t)




It is symmetrical about the horizontal. 


It is symmetrical about the vertical. 


Rotationally symmetric alpha degree about the pole









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