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Algebra

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 Joined: 15 Sep 2011 Post: 17
17 Sep 2011 22:19:54 IST
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What is the range of cos(cosx)?
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

What is the range of cos(cosx)?

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
18 Sep 2011 07:30:46 IST
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the maximum value of cosx = 1 at 2npi and its minimum value is  -1 at (2n+1)pi.

so we put this cos(cosx).

we get the maximum value to be cos(cos0). we don't consider cos(cos180) = cos1 for the maximum value. it will be lesser than 1.

yeah for the minimum value we take cos(cos90) or cos(cos180) = cos1. cos(-x) = cosx.

as x increases from 0 to 90 cosine decreases.

the range is form the maximum value to the minimum value. :-)

New kid on the Block

Joined: 20 Sep 2011
Posts: 6
20 Sep 2011 17:53:33 IST
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-1 to +1

New kid on the Block

Joined: 12 Aug 2011
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22 Sep 2011 16:23:13 IST
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Assume it to be a machine first cosx lies from -1 to 1 then it is domain for cosx again hence range is (cos1, 1)@mr iit:u r is wrong

Forum Expert
Joined: 23 Jan 2007
Posts: 7958
4 Apr 2012 21:19:05 IST
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Input of cos(cosx) is cosx which lies between -1 and 1.

Since cos(-x) = cosx it is sufficient to solve for cosx varying from 0 to 1.

from 0 to 1 cosx is decreasing function and hence its maximum will occur at cosx=0 and minimum at cosx=1

so cos(cosx) will vary from cos(1) to cos(0)  i.e.  (cos1 , 1)

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
6 Apr 2012 13:20:41 IST
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@ Hemag @mr iit I think your answers are wrong.. can you please show me where does cos(cosx) becomes zero?? The answer should be [cos1,1]

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