Understanding the Spherical Polar Coordinate System

Mathematics
[caption id="attachment_9496" align="alignright" width="480"] A cone in the spherical polar coordinate system. CC-SA 3.0 Unported by Lantonov[/caption] Do you have a basic knowledge of the spherical polar coordinate system? A coordinate system provides a way to describe and plot math functions using two or three variables. If there are two variables the graph is 2D. If there are three variables, the graph is 3D. The Cartesian Coordinate System The most familiar coordinate system is the Cartesian coordinate system. Typical variable names are x and y in 2D (although variables can have any name), and x, y, and z in 3D. Every point of every 2D function has a unique value in (x, y). Every 3D function similarly has a unique value in (x, y, z). The Polar Coordinate System This…
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Introduction to Polar Coordinates

Mathematics
[caption id="attachment_25281" align="alignright" width="403"] Polar rose: r = 2 sin (4*θ)[/caption]Frequently used in analytical geometry is the standard 2-dimensional x, y coordinate system called the Cartesian coordinate system (named after famous mathematician, René Descartes). It's time to branch out to a different system, the polar coordinates system. In fact, there are any of a number of ways of locating points in 2-D space. Conversion from Cartesian Coordinates The polar coordinates system utilizes an angle and a radius. It is relatively simple to change from the x-y system to an r-θ system. Drawing a circle centered at the origin on an x-y plane and then drawing a right triangle with the radius of the circle equaling r, then by definition, the side adjacent to the angle divided by the hypotenuse (longest…
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