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 Trigonometry Trigonometry Math Forum

 November 19th, 2017, 09:59 PM #1 Newbie   Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0 Write 2sin(3x)cos(x) as a sum Please help me out with this. I'm new to the product-to-sum formulas and the 2sin is throwing me off. Write 2sin(3x)cos(x) as a sum November 19th, 2017, 10:17 PM #2 Newbie   Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0 Nevermind.. I was overthinking again. The 2 goes away because in product-to-sum you multiply by 1/2. November 20th, 2017, 07:26 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The obvious thing to have done would be to ignore the "2", expand sin(3x)cos(x) and then multiply by 2. For sin(3x)cos(x), I would use the fact that sin(A+ B)= sin(A)cos(B)+ cos(A)sin(B). It is also true, then, that sin(A- B)= sin(A)cos(B)- cos(A)sin(B). Adding 2sin(A)cos(B)= sin(A+ B)+ sin(A- B). Here, 2sin(3x)cos(x)= sin(3x+ x)+ sin(3x- x)= sin(4x)+ sin(2x). Thanks from JPow November 20th, 2017, 08:02 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 The relevant product-to-sum formula is given as $2\sin A\cos B = \sin(A + B) + \sin(A - B)$ in the book I use. Thanks from JPow November 21st, 2017, 08:32 AM #5 Newbie   Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0 Thanks for the replies. It makes a lot more sense to me now. Tags 2sin3xcosx, sum, write Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Speed Algebra 3 March 5th, 2014 12:51 PM yogazen2013 Algebra 5 August 6th, 2013 02:38 AM chessy Calculus 8 February 2nd, 2011 09:31 AM tinyone Algebra 14 October 27th, 2010 08:38 PM conjecture Algebra 1 July 17th, 2008 12:45 AM

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