Trigonometric functions graphs

A function may be represented by a graph, which is a picture of how the value of the function (dependent variable) changes when the independent variable changes. Some of the more common periodic functions include the sawtooth, the square wave, and the trigonometric functions (sine, cosine, and tangent) (Figure 1). 

There are several families of trigonometric functions. We have already discussed them in Chapter 2. You should be familiar with the graphs of the trigonometric functions that are shown in Figs. 2.2 through 2.4. 

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. 

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