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 Trigonometry Trigonometry Math Forum

 August 3rd, 2016, 03:28 PM #1 Member   Joined: Jul 2016 From: Usa Posts: 59 Thanks: 3 Exact values? Cos^-1 (cos (-pi/3)) couldn't it be either 2pi/3 or 4pi/3? Tan^-1(1) couldn't it be either 7pi/4 or 3pi/4 ? Can there be more than 1 exact value? August 3rd, 2016, 04:38 PM   #2
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Quote:
 Originally Posted by Pete23 Cos^-1 (cos (-pi/3)) couldn't it be either 2pi/3 or 4pi/3?
neither ...

$Cos^{-1}\bigg[\cos\left(-\dfrac{\pi}{3}\right)\bigg] = Cos^{-1}\left(\dfrac{1}{2}\right) = \dfrac{\pi}{3}$

Quote:
 Tan^-1(1) couldn't it be either 7pi/4 or 3pi/4 ?
no ... $Tan^{-1}(1) = \dfrac{\pi}{4}$

Quote:
 Can there be more than 1 exact value?
no, the inverse trig functions yield a single value because they are functions ...

if the problem were stated ...

Given that $\tan{x} = 1$, then for $0 \le x < 2\pi$, determine all value(s) of $x$ ... $x = \dfrac{\pi}{4}$ and $x = \dfrac{5\pi}{4}$ August 3rd, 2016, 05:06 PM   #3
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Quote:
 Originally Posted by skeeter neither ... $Cos^{-1}\bigg[\cos\left(-\dfrac{\pi}{3}\right)\bigg] = Cos^{-1}\left(\dfrac{1}{2}\right) = \dfrac{\pi}{3}$ no ... $Tan^{-1}(1) = \dfrac{\pi}{4}$ no, the inverse trig functions yield a single value because they are functions ... if the problem were stated ... Given that $\tan{x} = 1$, then for $0 \le x < 2\pi$, determine all value(s) of $x$ ... $x = \dfrac{\pi}{4}$ and $x = \dfrac{5\pi}{4}$
But doesnt cos^-1 (x)= cos theta -(x)? August 3rd, 2016, 05:07 PM #4 Member   Joined: Jul 2016 From: Usa Posts: 59 Thanks: 3 What does that -1 exponent even represent then? August 3rd, 2016, 05:15 PM   #5
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Quote:
 Originally Posted by Pete23 What does that -1 exponent even represent then?
it's not an exponent ... it is notation for an inverse function

the inverse of $f(x)$ is notated $f^{-1}(x)$

an inverse swaps x and y values ... in other words, if $f(1)=2$, then $f^{-1}(2)=1$

I'm not a big fan of the $-1$ notation, which is why I prefer "arc" notation ...

$y =\sin{x} \implies x = \arcsin{y}$ August 3rd, 2016, 06:41 PM #6 Member   Joined: Jul 2016 From: Usa Posts: 59 Thanks: 3 Thanks! August 3rd, 2016, 06:42 PM #7 Member   Joined: Jul 2016 From: Usa Posts: 59 Thanks: 3 I was way over complicating what I had to do. Tags exact, values 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 alishab Trigonometry 8 December 11th, 2015 06:31 PM Qutyberry Trigonometry 8 May 3rd, 2014 08:32 PM mtt0216 Algebra 16 March 8th, 2010 04:09 PM gretchen Algebra 1 April 1st, 2007 01:01 AM hatcher777 Algebra 12 January 13th, 2007 03:43 AM

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