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January 24th, 2012, 01:30 AM   #1
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Trigonometric inequalities problem

So I have problem solving this two trigonometric inequalities

sinx+cox+sin2x>1

tg(x+pi/5)<sqrt(3)

Please help and if you can post the procedure of solving this inequalities
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January 24th, 2012, 02:31 AM   #2
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Re: Trigonometric inequalities problem

Quote:
sinx+cox+sin2x>1
Is that 'cos' or 'cot'?
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January 24th, 2012, 02:45 AM   #3
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Re: Trigonometric inequalities problem

Quote:
tg(x+pi/5)<sqrt(3)






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January 24th, 2012, 03:05 AM   #4
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Re: Trigonometric inequalities problem

oh,its cosx
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January 24th, 2012, 10:22 AM   #5
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Re: Trigonometric inequalities problem

We are given:













Solving the quadratic equation:





Assuming x is real, we must discard the root whose magnitude is greater than 1, so we have:



Checking the interval given by:





Using , we find by substitution into the quadratic inequality:







Thus, we find:

where
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January 24th, 2012, 03:27 PM   #6
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Re: Trigonometric inequalities problem

THANK YOU
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January 24th, 2012, 05:44 PM   #7
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Re: Trigonometric inequalities problem

Quote:
Originally Posted by niki500
tg(x+pi/5)<sqrt(3)








These values can be obtained by solving





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January 25th, 2012, 01:06 AM   #8
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Re: Trigonometric inequalities problem

Ok,so I have these two more inequalities to solve and Im done

2sinx*sin2x*sin3x<sin4x

sinx*cos5x<sin9x*cos3x
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January 25th, 2012, 01:17 AM   #9
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Re: Trigonometric inequalities problem

Have you made any attempt at solving them?
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January 25th, 2012, 01:37 AM   #10
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Re: Trigonometric inequalities problem

Yes I did for the first one I come to this sin2xcos3xcosx>0 and for the second one sin12x>-sin4x and dont know how to solve it further
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