My Math Forum Simplifying trig expression

 Trigonometry Trigonometry Math Forum

 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?) $\cot (\frac{2\pi }{3} - x)$ 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: 20,629 Thanks: 2077 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 $\cot x= \tan (\frac{\pi }{2} - x)$ 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 $\cot x= \tan (\frac{\pi }{2} - x)$ $\cot (\frac{2\pi }{3} - x)= \tan (\frac{2\pi }{3} - (\frac{\pi}{2} - x))$ $= \tan (\frac{2\pi }{3} - \frac{\pi}{2} + x)$ $= \tan (\frac{4\pi }{6} - \frac{3\pi}{6} + x)$ $= \tan (\frac{\pi }{6} + x)$ Is this how it's done? I checked on a calculator and it says it's $-\tan (\frac{\pi }{6} - x)$ I know $-\tan x= tan(-x)$ but $-\tan (\frac{\pi }{6} - x)= \tan (-\frac{\pi }{6} + x)$ 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: 521

Math Focus: Calculus/ODEs
Re: Simplifying trig expression

Quote:
 Originally Posted by daigo ... Since $\cot x= \tan (\frac{\pi }{2} - x)$ $\cot (\frac{2\pi }{3} - x)= \tan (\frac{2\pi }{3} - (\frac{\pi}{2} - x))$ ...I don't know what's going on or where I'm going wrong...
You need to write:

$\cot$$\frac{2\pi }{3}-x$$=\tan$$\frac{\pi}{2}-\(\frac{2\pi }{3}-x$$\)$

 June 30th, 2012, 11:05 AM #5 Senior Member   Joined: Jan 2010 Posts: 205 Thanks: 0 Re: Simplifying trig expression Oh, $(\frac{2\pi}{3} - x)$ 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: 521 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: 521 Math Focus: Calculus/ODEs Re: Simplifying trig expression The co-function identity: $\cot$$\theta$$=\tan$$\frac{\pi}{2}-\theta$$$ tells you to take the argument ? on the left side and place it in the right side using the identity. Hence: $\cot$$f(x)$$=\tan$$\frac{\pi}{2}-f(x)$$$

 Tags expression, simplifying, trig

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Polaris84 Trigonometry 1 October 17th, 2013 09:34 AM nikki1234 Algebra 2 May 14th, 2011 09:45 PM Gustav Algebra 1 October 10th, 2010 12:51 AM paulw Applied Math 3 September 23rd, 2010 11:22 AM finmorhouse Linear Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top