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 Post subject: monotonocity
PostPosted: Sun, 6 May 2012 18:48:51 UTC 
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show that \frac{ sin(x+a)}{sin(x+b)} varies monotonically in any interval having no points of discontinuity of the function

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 Post subject: Re: monotonocity
PostPosted: Sun, 6 May 2012 19:09:01 UTC 
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mun wrote:
show that \frac{ sin(x+a)}{sin(x+b)} varies monotonically in any interval having no points of discontinuity of the function


What do you mean "varies monotonically" what does it mean for variation to be monotonic? Do you just mean the function is monotone?

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 Post subject: Re: monotonocity
PostPosted: Sun, 6 May 2012 19:11:36 UTC 
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Shadow wrote:
mun wrote:
show that \frac{ sin(x+a)}{sin(x+b)} varies monotonically in any interval having no points of discontinuity of the function


What do you mean "varies monotonically" what does it mean for variation to be monotonic? Do you just mean the function is monotone?

sir it is the exact statement written in book.may be they are asking for monotonocity in a gap of 180 degree.?

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 Post subject: Re: monotonocity
PostPosted: Sun, 6 May 2012 23:03:04 UTC 
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The intervals have end points where x+b = π (180°). To answer the question the derivative of the function should not = 0 in any such interval.


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 Post subject: Re: monotonocity
PostPosted: Sun, 6 May 2012 23:36:07 UTC 
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mathematic wrote:
The intervals have end points where x+b = π (180°). To answer the question the derivative of the function should not = 0 in any such interval.


Assuming he means just monotone, then yes, this is correct. I'd definitely like clarification from a teacher or something, as variation has its own definition in analysis.

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 Post subject: Re: monotonocity
PostPosted: Mon, 7 May 2012 05:16:25 UTC 
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mun wrote:
show that \frac{ sin(x+a)}{sin(x+b)} varies monotonically in any interval having no points of discontinuity of the function


Apply the Quotient Rule and observe the numerator...

Spoiler:
For f(x)=\frac{\sin(x+a)}{\sin(x+b)},

f'(x)=\frac{\sin(b - a)}{\sin^2(x+b)}.

The numerator is a constant and the denominator is always positive (except when it's zero, but that's when the original function is discontinuous)...


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