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 February 26th, 2011, 09:18 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, 02:10 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond Re: Trigonometry a = 49/?(2), tan(?) = ?(2) - 1.
 February 27th, 2011, 03:42 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, 05:34 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,635 Thanks: 2080 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, 10:20 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, 10:34 PM   #6
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Re: Trigonometry

Quote:
 Originally Posted by johnny Could you post your solution, greg1313?

Nice to see it solved.

 March 1st, 2011, 06:58 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,635 Thanks: 2080 Given the above work, it's straightforward to find tan(?).

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