anonymous
  • anonymous
y = 2tan(theta) . Find the value of tangent, then double it. It's a table with pi/6 through 2pi
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
Can you post a screenshot of the full problem?
anonymous
  • anonymous
yeah, just one moment
anonymous
  • anonymous
sorry my computer is super slow

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anonymous
  • anonymous
1 Attachment
jim_thompson5910
  • jim_thompson5910
that's fine
jim_thompson5910
  • jim_thompson5910
ah, I see now
jim_thompson5910
  • jim_thompson5910
so what you do is replace \(\Large \theta\) (greek letter theta) with the numbers in the top row Use the unit circle or a table to find that \[\Large \tan(\theta) = \tan(0) = 0\] \[\Large \tan(\theta) = \tan\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{3}\] \[\Large \tan(\theta) = \tan\left(\frac{\pi}{4}\right) = 1\] etc etc
jim_thompson5910
  • jim_thompson5910
then you double each result \[\Large 2*\tan(\theta) = \tan(0) = 2*0 = 0\] \[\Large 2*\tan(\theta) = 2*\tan\left(\frac{\pi}{6}\right) = 2*\frac{\sqrt{3}}{3} = \frac{2\sqrt{3}}{3}\] \[\Large 2*\tan(\theta) = 2*\tan\left(\frac{\pi}{4}\right) = 2*1 = 2\] etc etc
anonymous
  • anonymous
so it's just the coordinate points ?
jim_thompson5910
  • jim_thompson5910
yeah the y coordinates of each point on the graph of y = tan(x)
jim_thompson5910
  • jim_thompson5910
2*tan(x) I mean
anonymous
  • anonymous
ugh thank you, you're a life saver
jim_thompson5910
  • jim_thompson5910
you're welcome
anonymous
  • anonymous
wait how'd you get \[\pi/4 \] to be 1
jim_thompson5910
  • jim_thompson5910
tan of pi/4 is 1
jim_thompson5910
  • jim_thompson5910
if you look at the unit circle, you'll find that sine and cosine have the same value at pi/4 sin(pi/4) = cos(pi/4)
jim_thompson5910
  • jim_thompson5910
because of that and because tangent = sine/cosine, the two equal values divide to 1
anonymous
  • anonymous
oooooooh okay, i get it now
jim_thompson5910
  • jim_thompson5910
I'm glad it's making more sense
anonymous
  • anonymous
Yeah I'm the worst at trigonometry lol
jim_thompson5910
  • jim_thompson5910
I'm sure with more practice, you'll get better at it
anonymous
  • anonymous
this is my third year learning this and I still haven't learned it :/
jim_thompson5910
  • jim_thompson5910
then a different approach is needed
anonymous
  • anonymous
yes, badly so for pi/3 , would it be radical 3 ? or do the 2's not cancel out ?
jim_thompson5910
  • jim_thompson5910
the 2s will cancel leaving sqrt(3), correct
anonymous
  • anonymous
Okay, I just wanted to make sure cause I've seen it where the 2's aren't being canceled out
anonymous
  • anonymous
and since I'm doubling it, would it be \[2\sqrt{3}\] or ?
jim_thompson5910
  • jim_thompson5910
I'd have to see the problem (where you didn't see the 2s cancel), but you should have this \[\Large \tan\left(\theta\right) = \frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\frac{\pi}{3}\right)}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}/2}{1/2}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\times\frac{2}{1}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{\cancel{2}}\times\frac{\cancel{2}}{1}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \sqrt{3}\]
jim_thompson5910
  • jim_thompson5910
yes, \[\Large 2\tan\left(\frac{\pi}{3}\right) = 2\sqrt{3}\]
anonymous
  • anonymous
Okay, I think I'm getting a little more. I saw it on some website and it was a table like I'm filling out and the 2's weren't canceled out
jim_thompson5910
  • jim_thompson5910
hmm, strange
anonymous
  • anonymous
but it just makes sense to cancel them out to me so I figured whoever made that table just forgot that step maybe?
jim_thompson5910
  • jim_thompson5910
that's possible
jim_thompson5910
  • jim_thompson5910
even teachers who write the problems and examples make typos
anonymous
  • anonymous
I know many lol. But anyways, thank you so much
jim_thompson5910
  • jim_thompson5910
sure thing

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