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 December 11th, 2016, 05:27 PM #1 Newbie   Joined: Dec 2016 From: USA Posts: 11 Thanks: 0 Evaluate exaclty tan(2pi/3-2009pi)
December 11th, 2016, 05:33 PM   #2
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Quote:
 Originally Posted by Kingsiso tan(2pi/3-2009pi)
Tangent has a period of $\displaystyle \pi$. That means $\displaystyle tan(x + k \pi ) = tan(x)$ for any integer k. So how many multiples of $\displaystyle \pi$ are there in $\displaystyle 2009 \pi$? (Yes, it's almost a trick question.)

-Dan

 December 11th, 2016, 05:54 PM #3 Newbie   Joined: Dec 2016 From: USA Posts: 11 Thanks: 0 You just confused me, I'm also impressed by that vocabulary
December 11th, 2016, 06:30 PM   #4
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Quote:
 Originally Posted by Kingsiso You just confused me, I'm also impressed by that vocabulary
for $k$ = any integer, $\tan(x + k\pi) = \tan{x}$ because the tangent function has a period (repeats itself) every $\pi$ units.

note the attached graphs ... see any difference?
Attached Images
 tanx.jpg (14.2 KB, 0 views) tanx+100pi.jpg (15.5 KB, 0 views) tanx+2009pi.jpg (15.7 KB, 0 views)

 December 11th, 2016, 07:03 PM #5 Newbie   Joined: Dec 2016 From: USA Posts: 11 Thanks: 0 Thanks guy!

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