Plane polar coordinates transformation equations

Changing from plane polar coordinates to Cartesian coordinates is an example of transformation of coordinates, and can be done by using the equations... 

These functions are called circular or trigonometric functions. Note that Equations (2-25) are just the transformation Equations (1-4) with r = 1. It is interesting to compare the graphs of functions, such as sin 0 and cos 0, in linear coordinates (coordinates in which 0 is plotted along one axis) to those in plane polar coordinates. Consider, for example, the equation r = A cos 0y where A is a constant. Such an equation can be used to describe the wave properties of p-type atomic orbitals in two dimensions. The functional dependence of r upon 0 can be seen in Table 2-1. 

Therefore, every point (x, y) can be specified by assigning to it a value for r and a value for 6. This type of graphical representation is called a plane polar coordinate system. In this coordinate system, points are designated by the notation (r, ). The Equations (1-4) are known as transformation equations they transform the coordinates of a point from polar coordinates to Cartesian (linear) coordinates. The reverse transformation equations can be found by simple trigonometry. 

Recall from Chapter 1 that the transformation and reverse transformation equations to plane polar coordinates are... 

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