Chapter 5 explores graphical transformations, the effects that constants have on the graphs of functions depending upon their placement within the function. For example, multiplying by a constant within a function stretches or compresses that function, whereas adding or subtracting a value within the function shifts its graph but does not affect its shape. In this chapter, you are introduced to the graphs of the four remaining trigonometric functions, and you apply the same transformations to these slightly more complex graphs.
Sine and cosine are defined for all real numbers, but that’s not true for the other four trig functions. Because tangent, cotangent, secant, and cosecant are all defined as quotients containing sine and/or cosine, graphs in this chapter are a little more complicated. Whenever quotients are involved, you have to worry about dividing by zero, which is not allowed.
Any time the denominator of a trig function could equal zero, you have to create an invisible fence in the graph—like the kind people dig into their yards to keep their dogs from running away. These “fences” are vertical lines called asymptotes, which functions (like dogs) can approach but not cross.