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 Algebra Pre-Algebra and Basic Algebra Math Forum

 December 21st, 2007, 04:34 PM #1 Newbie   Joined: Dec 2007 Posts: 5 Thanks: 0 trignometric identities. ((4sin x)(sin y))/((4cos x)(cos y)) = (tan x)(tan y) How is that trig function equal to those tan functions? December 21st, 2007, 04:54 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 In general, tan u = sin u / cos u. Proof: In a unit circle, let sin u = y/r, and cos u = x/r. Also, we will say that tan u = y/x. We can algebraically do some division, where (y/r)/(x/r) = y/x, hence sin u / cos u = tan u. ((4sin x)(sin y))/((4cos x)(cos y)) = ((sin x)(sin y))/((cos x)(cos y)) = ((sin x)/(cos x))(sin y)/(cos y)) = (tan x)(tan y) Q. E. D. December 21st, 2007, 09:28 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,933 Thanks: 2207 You mean the circle with equation x² + y² = r². That's not the same (position or radius) as "a unit circle". December 22nd, 2007, 01:09 PM   #4
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 Originally Posted by johnny In general, tan u = sin u / cos u. Proof: In a unit circle, let sin u = y/r, and cos u = x/r. Also, we will say that tan u = y/x. We can algebraically do some division, where (y/r)/(x/r) = y/x, hence sin u / cos u = tan u. ((4sin x)(sin y))/((4cos x)(cos y)) = ((sin x)(sin y))/((cos x)(cos y)) = ((sin x)/(cos x))(sin y)/(cos y)) = (tan x)(tan y) Q. E. D.
Thank YOU! December 22nd, 2007, 04:12 PM #5 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 You're welcome, and the x^2 + y^2 = r^2 should've been replaced over unit circle, so skipjack is right on that part. On the algebraic part, I think I showed you correctly, where the obvious general equation tan u = sin u / cos u comes along. Tags identities, trignometric 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 ashu Calculus 15 September 24th, 2012 12:24 AM layd33foxx Calculus 1 February 21st, 2012 05:33 PM prashantakerkar Trigonometry 5 November 15th, 2011 12:20 AM jatt-rockz Trigonometry 5 November 10th, 2011 12:17 PM Nikki White Algebra 2 October 26th, 2010 01:34 PM

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