My Math Forum Smallest Asymptote of a tan function

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 May 27th, 2018, 05:50 AM #1 Newbie   Joined: May 2018 From: Germany Posts: 2 Thanks: 0 Smallest Asymptote of a tan function Hi guys. How does one go about finding the smallest asymptote of this function. f(x) = tan(-9x+8 ) where x>=0 (in radians)
 May 27th, 2018, 07:17 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,285 Thanks: 1681 For x = (8 - 5pi/2)/9, -9x + 8 = 5pi/2, and so tan(-9x + 8) is undefined. There's no asymptote closer to the origin (even if negative values of x are allowed).
 May 27th, 2018, 07:19 AM #3 Newbie   Joined: May 2018 From: Germany Posts: 2 Thanks: 0 where did you get the 5pi/2 from? or rather, where did you get the whole x equation from?
 May 27th, 2018, 11:29 AM #4 Global Moderator   Joined: Dec 2006 Posts: 19,285 Thanks: 1681 As -9x + 8 needs to be an odd multiple of pi/2, I selected the odd multiple of pi/2 that's closest to 8 and then found the corresponding value of x, which happened to be non-negative, as required.

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