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May 23rd, 2018, 08:48 PM   #1
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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.
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May 23rd, 2018, 09:33 PM   #2
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$\{x\} \in [0,1)$

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.
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May 24th, 2018, 09:29 AM   #3
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Quote:
Originally Posted by romsek View Post
$\{x\} \in [0,1)$

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.
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May 24th, 2018, 10:09 AM   #4
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Quote:
Originally Posted by happy21 View Post
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.
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May 24th, 2018, 08:01 PM   #5
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Without looking at tables and calculator...this value can be obtained...!
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May 24th, 2018, 08:10 PM   #6
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Quote:
Originally Posted by happy21 View Post
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

$\left[1,~\dfrac{1}{\cos(1)}\right) = [1,\sec(1))$
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May 24th, 2018, 08:20 PM   #7
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Thx.
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