My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 25th, 2012, 12:59 PM   #1
Newbie
 
Joined: Aug 2011

Posts: 24
Thanks: 0

Equivalent Trig Expressions

Given that cot (13pi/14)= tan z, find angle z.
So I used cot x=tan(pi/2-x), and I got the answer -3pi/7, but the answer says it's positive, so I am confused.
Thanks in advance!
Pumpkin99 is offline  
 
January 25th, 2012, 01:20 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,963
Thanks: 1148

Math Focus: Elementary mathematics and beyond
Re: Equivalent Trig Expressions

$\displaystyle \tan\left(x + \frac{\pi}{2}\right) = -\cot(x)$

$\displaystyle \frac{13\pi}{14} + \frac{\pi}{2} = \frac{10\pi}{7}$

$\displaystyle -\tan(x) = \tan(-x) \Rightarrow \tan\left(-\frac{10\pi}{7}\right) = \tan\left(-\frac{3\pi}{7}\right),\,z = - \frac{3\pi}{7}$

Last edited by skipjack; August 24th, 2019 at 04:24 PM.
greg1313 is offline  
January 25th, 2012, 01:36 PM   #3
Newbie
 
Joined: Jan 2012

Posts: 9
Thanks: 0

Re: Equivalent Trig Expressions

Yes, it is correct and tg must be negative because cotangent is in II. Quadrant. Maybe in your book there is positive solution because if you add 2pi to -3pi/7 you get the same angle 2pi+(-3pi/7)=11pi/7 but in positive direction.

Last edited by skipjack; August 24th, 2019 at 04:25 PM.
niki500 is offline  
January 25th, 2012, 02:52 PM   #4
Newbie
 
Joined: Aug 2011

Posts: 24
Thanks: 0

Re: Equivalent Trig Expressions

thank you!
Pumpkin99 is offline  
January 25th, 2012, 03:34 PM   #5
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,963
Thanks: 1148

Math Focus: Elementary mathematics and beyond
Re: Equivalent Trig Expressions

More accurately, $\displaystyle z = -\frac{3\pi}{7} + k\pi,\,k \in \mathbb{Z}$

Last edited by skipjack; August 24th, 2019 at 04:26 PM.
greg1313 is offline  
August 24th, 2019, 04:30 PM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 20,969
Thanks: 2219

I suspect that the book's answer was $4\pi$/7.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
equivalent, expressions, trig



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Functional Krockner Delta Equivalent Expressions 667 Number Theory 12 January 26th, 2014 01:09 AM
Solving limits containing trig expressions PhizKid Calculus 9 August 29th, 2012 01:14 PM
[TRIG] Equivalent Expression Help RMG46 Algebra 10 June 15th, 2010 08:26 AM
Equivalent algebric expressions - Help please roger911 Calculus 2 June 19th, 2009 03:15 PM
Simplifying Trig. Expressions TyRReLL2oo9 Algebra 10 April 6th, 2009 03:45 AM





Copyright © 2019 My Math Forum. All rights reserved.