Graphs of Tangent and Cotangent

    This topic presents the graphs of the tangent and cotangent 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 tangent and cotangent are detailed including the period (portion that repeats) and the phase shift (horizontal shift).

Proposition (Tangent Graph) The tangent function has the following graph



Notice that the tangent function has zeros at (written as where is any integer) and does not have a maximum nor a minimum value.

Proposition (Cotangent Graph) The cotangent function has the following graph



Notice that the cotangent function has zeros at and does not have a maximum nor a minimum value.

Proposition (Graphs of Tangent and Cotangent) Period. If or then the graph has period

Example (Graphs of Tangent and Cotangent) Find the period of the graph of and sketch the graph.

    Solution. The period is and here is the graph:




Example (Graphs of Tangent and Cotangent) Find the period of the graph of and sketch the graph.

    Solution. The period is and here is the graph:



Notice that the minus sign reflects the graph through the -axis.

Proposition (Graphs of Tangent and Cotangent) Phase Shift. If or then the graph has phase shift of

Example (Graphs of Tangent and Cotangent) Find the phase shift and period of and sketch the graph.

    Solution. The phase shift is and the period   . Here is the graph:
    




Example (Graphs of Tangent and Cotangent) Find the phase shift and period of and sketch the graph.  

    Solution. The phase shift is and the period is Here is the graph:
    

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Graphs Of Tangent And Cotangent
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/graphs-of-tangent-and-cotangent.html