Hobbies And Interests
The Polar Coordinate System
Polar graphing makes use of the polar coordinate system. This system locates points by specifying how far away from the origin they are and in what direction. The direction of a point is measured with the angle made by a line running from the origin to that point and the positive x-axis. The distance is usually represented by the letter r, and the angle by the Greek letter theta.
Polar Graph Paper
Polar graphs are most easily done on polar graph paper. This is paper that has been imprinted with a series of concentric circles. Each circle differs in size from the next by the same amount. The circles are crossed by several lines, all intersecting at the center of the circles. These lines are each set at a different angle, and they are all marked with the angle at which they are set. The circles measure the distance from the center, the lines mark the angles.
Polar Coordinate Transformations
It is possible to graph polar coordinates onto a Cartesian-style graph. To find the x-coordinate of a point in polar coordinates, multiply r by the cosine of theta. To find the y-coordinate, multiply r by the sine of theta. To use polar graphing for an equation in Cartesian coordinates, divide y by x and take the inverse tangent of the result. This result is equal to theta. Square both x and y and add the squares together. Take the square root of the result. This result is equal to r.
Uses of Polar Graphing
Polar graphing is more appropriate than Cartesian graphing when describing rotary or circular motion. The equations describing such motion are very simple in polar coordinates, but very complex in Cartesian coordinates. Polar graphing is also appropriate for plotting data from radar and sonar, which is in the form of distances recorded at different angles.