Graphs of Secant and Cosecant

    This topic presents the graphs of the secant and cosecant functions. These graphs can be obtained by plotting points or using a knowledge of the values of the trigonometric functions, reference angles, and symmetry. The basic transformations of the secant and cosecant are detailed including the amplitude (height), the period (portion that repeats), and the phase shift (horizontal shift).

Proposition (Secant Graph) The secant function has the following graph




Notice that the secant function does not have any zeros nor any absolute maximum or minimum values.

Proposition (Cosecant Graph) The cosecant function has the following graph



Notice that the cosecant function does not have any zeros nor any absolute maximum or minimum values.

Proposition (Graphs of Secant and Cosecant) The graphs of and can be obtained by graphing and (respectively) and then taking the reciprocal of each -coordinate.

Example (Graphs of Secant and Cosecant) Find the phase shift, amplitude and period of Sketch the graph.

    Solution. The phase shift is the amplitude is the period of and here is the graph:



Thus to graph we take the reciprocal of each -coordinate and obtain:





Example (Graphs of Secant and Cosecant) Find the phase shift, amplitude and period of Sketch the graph.

    Solution. The phase shift is the amplitude is the period of and here is the graph:
    


Thus to graph we take the reciprocal of each -coordinate and obtain:

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Graphs Of Secant And Cosecant
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/graphs-of-secant-and-cosecant.html