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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: 20,636 Thanks: 2080 
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: 20,636 Thanks: 2080 
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 nonnegative, as required.


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asymptote, function, smallest, tan, trigonometric functions 
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