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 February 26th, 2013, 05:00 AM #1 Senior Member   Joined: Sep 2012 Posts: 201 Thanks: 1 Trig identities So I have this question fairly simple, I would say, but my issue is I can't actual visualise what it is asking so to speak; I will explain. Question: Given that x is an acute, find tan x if . So I first went back to the unit circle to try and give a better understanding. From this I get the 2 identities and . So this is where I am sort of winging it so to speak. Because I have a in the equation my tan would look like the , I then sub the identities in and solve; have checked the answer in back of the book, which gives the correct answer, my concern is do I have the right method for working the question out, or have I gone wrong and by some luck got the right answer? Big thanks in advance. February 26th, 2013, 05:44 AM #2 Global Moderator   Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Trig identities Using your reasoning, you should have that cos^2 = 1 - 3/4 = 1/4. So tan^2 = sin^2/cos^2 = (3/4)/(1/4) = 3. Tan(x) is therefore the square root of 3. Here is where the assumption that x is acute comes in. Of course, knowing that x is acute is enough to conclude that sin(x) = sqrt(3)/2, whence tan(x) = sqrt(3) immediately. February 26th, 2013, 05:54 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 If x is acute, tan(x) is positive. tan�(x) = sin�(x)/cos�(x) = sin�(x)/(1 - sin�(x)) = (3/4)/(1 - (3/4)) = 3, so tan(x) = ?3. Alternatively, cot�(x) = csc�(x) - 1 = 1/sin�(x) - 1 = 4/3 - 1 = 1/3, so cot(x) = 1/?3. Hence tan(x) = ?3. For a third method, x must be the angle in a right-angled triangle with leg opposite angle x of length ?3, and with hypotenuse of length 2. By Pythagoras, the leg adjacent to the angle x has length 1. Hence tan(x) = ?3. February 26th, 2013, 08:05 AM   #4
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Re: Trig identities

Hello, taylor_1989_2012!

Quote:

Code:
                  *
* *
*   *  _
2 *     * /3
*       *
* x       *
*  *  *  *  *
adj March 4th, 2013, 02:05 AM #5 Senior Member   Joined: Sep 2012 Posts: 201 Thanks: 1 Re: Trig identities Thanks for all the replies, once again big help, and thanks again. Tags identities, trig 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 mathatesme Trigonometry 3 January 13th, 2014 04:20 AM Gokias Trigonometry 10 July 13th, 2011 02:14 PM jordanshaw Algebra 1 October 15th, 2010 11:47 PM jordanshaw Algebra 4 October 15th, 2010 01:28 PM jelsier Algebra 2 May 25th, 2009 07:56 PM

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