Cartesian vs. Polar Coordinates
Main Concept
The Cartesian coordinate system is a two-dimensional coordinate system using a rectilinear grid:
The x and y coordinates of a point measure the respective distances from the point to a pair of perpendicular lines in the plane called the coordinate axes, which meet at the origin.
The polar coordinate system is a two-dimensional coordinate system using a polar grid:
The r and θ coordinates of a point P measure respectively the distance from P to the origin O and the angle between the line OP and the polar axis.
Points in the cartesian coordinate system and points in the polar coordinate system can be converted into each other via the formulae:
x=r⋅cosθ
y=r⋅sinθ
r =x2+y2
θ= arctany, x={arctanyx0<xarctanyx+πx<0, 0≤yarctanyx−πx<0, y<0π2x=0, y>0−π2x=0, y<00x=0,y=0
Click and or drag on the graph to change the point. Notice the difference between Cartesian and polar coordinates. Change between measuring the angle in degrees or radians using the radio buttons.
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