The FCS #tan_(fcs)(pix: pi) = tan (pix+ pi (tan (pix + pi tan (pix +...)#. How do you graph this FCS to reveal x-intercepts #0, +-1, +_2, +3|-...#?

1 Answer
A. S. Adikesavan
Jun 30, 2018

See graph and explanation.

Explanation:

As #y = tan_(fcs)( pix; pi ) = tan ( pi ( x + y ) ), inversely,

#pi ( x + y ) = kpi + tan ^(-1) y, k = 0, +-1, +-2, +-3, ...#.

So, upon setting #y = 0, x = 0, +-1, +-2, +-3, ...#

See graph for these x-intercepts.

graph{y - tan ( pi ( x + y )) = 0[-10 10 -2 2] }

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