My Math Forum Range of a function

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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: 2,122 Thanks: 1102 $\{x\} \in [0,1)$ 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. Thanks from happy21 and Maschke
May 24th, 2018, 09:29 AM   #3
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Quote:
 Originally Posted by romsek $\{x\} \in [0,1)$ 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.
How did you get 1.85...plz explain..
Thx.

May 24th, 2018, 10:09 AM   #4
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Quote:
 Originally Posted by happy21 How did you get 1.85...plz explain.. Thx.
...

$\dfrac{1}{\cos(1)} \approx 1.85$

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
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Quote:
 Originally Posted by happy21 Without looking at tables and calculator...this value can be obtained...!
if you're not allowed access to tables or calculator I would just leave it as

$\left[1,~\dfrac{1}{\cos(1)}\right) = [1,\sec(1))$

 May 24th, 2018, 08:20 PM #7 Senior Member     Joined: Jan 2012 Posts: 113 Thanks: 2 Thx.

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