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January 24th, 2012, 01:30 AM  #1 
Newbie Joined: Jan 2012 Posts: 9 Thanks: 0  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 
January 24th, 2012, 02:31 AM  #2  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: Trigonometric inequalities problem Quote:
 
January 24th, 2012, 02:45 AM  #3  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: Trigonometric inequalities problem Quote:
 
January 24th, 2012, 03:05 AM  #4 
Newbie Joined: Jan 2012 Posts: 9 Thanks: 0  Re: Trigonometric inequalities problem
oh,its cosx 
January 24th, 2012, 10:22 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs  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 
January 24th, 2012, 03:27 PM  #6 
Newbie Joined: Jan 2012 Posts: 9 Thanks: 0  Re: Trigonometric inequalities problem
THANK YOU 
January 24th, 2012, 05:44 PM  #7  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: Trigonometric inequalities problem Quote:
These values can be obtained by solving  
January 25th, 2012, 01:06 AM  #8 
Newbie Joined: Jan 2012 Posts: 9 Thanks: 0  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 
January 25th, 2012, 01:17 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: Trigonometric inequalities problem
Have you made any attempt at solving them?

January 25th, 2012, 01:37 AM  #10 
Newbie Joined: Jan 2012 Posts: 9 Thanks: 0  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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inequalities, problem, trigonometric 
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