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May 23rd, 2018, 08:48 PM  #1 
Senior Member Joined: Jan 2012 Posts: 113 Thanks: 2  Range of a function
Hello All, Can one please elaborate what will be the range of the following function: $\displaystyle f(x) = \frac{1}{\cos\left \{ x \right \}}$ where {x} = Fractional Part Function. Last edited by skipjack; May 23rd, 2018 at 10:40 PM. 
May 23rd, 2018, 09:33 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,042 Thanks: 1065 
$\{x\} \in [0,1)$ over that domain $\cos(x) \in (\cos(1),1]$ so $\dfrac{1}{\cos(x)} \in \left[1,\dfrac{1}{\cos(1)}\right) \approx \left[1,1.85\right)$ and this is periodic with a period of 1. 
May 24th, 2018, 09:29 AM  #3 
Senior Member Joined: Jan 2012 Posts: 113 Thanks: 2  
May 24th, 2018, 10:09 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,042 Thanks: 1065  ... $\dfrac{1}{\cos(1)} \approx 1.85$ Last edited by skipjack; May 24th, 2018 at 09:49 PM. 
May 24th, 2018, 08:01 PM  #5 
Senior Member Joined: Jan 2012 Posts: 113 Thanks: 2 
Without looking at tables and calculator...this value can be obtained...!

May 24th, 2018, 08:10 PM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 2,042 Thanks: 1065  
May 24th, 2018, 08:20 PM  #7 
Senior Member Joined: Jan 2012 Posts: 113 Thanks: 2 
Thx.


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