February 26th, 2011, 10:18 PM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Trigonometry
Let a > 0. If 25x²  ax + 12 = 0 has two roots sin 2? and cos 2?, determine the value of a and tan ?. 
February 27th, 2011, 03:10 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,913 Thanks: 1113 Math Focus: Elementary mathematics and beyond  Re: Trigonometry
a = 49/?(2), tan(?) = ?(2)  1.

February 27th, 2011, 04:42 PM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
The correct answer is a = 35 and tan ? = ½, ?. Could you post your solution, greg1313?

February 27th, 2011, 06:34 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,302 Thanks: 1974 
a/25 = sin 2? + cos 2?, so a²/625 = cos² 2? + 2sin 2? cos 2? + sin² 2? = 1 + 2(12/25) = 49/25. Hence a = 35. 
February 27th, 2011, 11:20 PM  #5 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
25x²  ax + 12 = 0 x²  a/25 · x + 12/25 = 0 ? and ? are roots of x²  (? + ?)x + ?? = 0 (? (x  ?)(x  ?) = x²  (? + ?)x + ??) ? a/25 = sin 2? + cos 2? and 12/25 = sin 2? cos 2? a²/25² = sin² 2? + 2sin 2? cos 2? + cos² 2? = 1 + 2 · 12/25 = 1 + 24/25 = 49/25 = 7²/5² a/25 = 7/5 = 1/5 · 7 ? a = 25/5 · 7 = 5 · 7 = 35 
February 27th, 2011, 11:34 PM  #6  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,913 Thanks: 1113 Math Focus: Elementary mathematics and beyond  Re: Trigonometry Quote:
Nice to see it solved.  
March 1st, 2011, 07:58 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,302 Thanks: 1974 
Given the above work, it's straightforward to find tan(?).


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