`y = tan^2 ((pix)/6) - 3` Find the x-intercepts of the graph.

Textbook Question

Chapter 5, 5.3 - Problem 47 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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x-intercepts are points where y=0, so we have to solve the equation

`tan^2((pix)/6)-3=0.`

This implies that `tan((pix)/6)=sqrt(3)` or `tan((pix)/6)=-sqrt(3),`

and this in turn implies

`(pix)/6=tan^(-1)(sqrt(3))+kpi` or `(pix)/6=tan^(-1)(-sqrt(3))+kpi,` `kinZZ.`

Take into account that `tan^(-1)(sqrt(3))=pi/3` and `tan^(-1)(-sqrt(3))=-pi/3`

The final answer:

`x=2+6k` and `x=-2+6k,` `kinZZ.`

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