Precalculus : Find the Equations of Vertical Asymptotes of Tangent, Cosecant, Secant, and Cotangent Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Find The Equations Of Vertical Asymptotes Of Tangent, Cosecant, Secant, And Cotangent Functions

Given the function , determine the equation of all the vertical asymptotes across the domain.  Let  be an integer.

Possible Answers:

Correct answer:


For the function , it is not necessary to graph the function.  The y-intercept does not affect the location of the asymptotes.

Recall that the parent function  has an asymptote at  for every  period.  

Set the inner quantity of  equal to zero to determine the shift of the asymptote.

This indicates that there is a zero at , and the tangent graph has shifted  units to the right.  As a result, the asymptotes must all shift  units to the right as well.  The period of the tangent graph is .

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