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June 30th, 2012, 10:24 AM  #1 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Simplifying trig expression
I have to simplify (or get it in terms of tan I guess?) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this? 
June 30th, 2012, 10:41 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
cot(A) = tan(?/2  A), so cot(2?/3  x) = tan(x  ?/6).

June 30th, 2012, 10:55 AM  #3 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Simplifying trig expression
I understand that Because it's a complementary angle, but I didn't know I could use that identity for this problem and I still don't really know why or how, but nonetheless I tried to create a ratio: Since Is this how it's done? I checked on a calculator and it says it's I know but Which is not the answer I got but the solution you provided so I don't know what's going on or where I'm going wrong I'm trying to visualize it because I think I work better with a visual but I don't know how to imagine this triangle 
June 30th, 2012, 11:00 AM  #4  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Simplifying trig expression Quote:
 
June 30th, 2012, 11:05 AM  #5 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Simplifying trig expression
Oh, is considered the 'x' value of that...I see now. That's kind of confusing; should different variables have been used for the 'x's?

June 30th, 2012, 11:07 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Simplifying trig expression
Exactly! That's why [color=#00BF00]skipjack[/color] used A, presumably to avoid that confusion. 
June 30th, 2012, 11:23 AM  #7 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Simplifying trig expression
Ohhh, I thought he just felt like picking 'A' for no reason...I didn't know it was supposed to differentiate the variable 'x' from the one in the other equation

June 30th, 2012, 11:31 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Simplifying trig expression
The cofunction identity: tells you to take the argument ? on the left side and place it in the right side using the identity. Hence: 

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