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anonymous

  • one year ago

y = 2tan(theta) . Find the value of tangent, then double it. It's a table with pi/6 through 2pi

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  1. jim_thompson5910
    • one year ago
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    Can you post a screenshot of the full problem?

  2. anonymous
    • one year ago
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    yeah, just one moment

  3. anonymous
    • one year ago
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    sorry my computer is super slow

  4. anonymous
    • one year ago
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  5. jim_thompson5910
    • one year ago
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    that's fine

  6. jim_thompson5910
    • one year ago
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    ah, I see now

  7. jim_thompson5910
    • one year ago
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    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

  8. jim_thompson5910
    • one year ago
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    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

  9. anonymous
    • one year ago
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    so it's just the coordinate points ?

  10. jim_thompson5910
    • one year ago
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    yeah the y coordinates of each point on the graph of y = tan(x)

  11. jim_thompson5910
    • one year ago
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    2*tan(x) I mean

  12. anonymous
    • one year ago
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    ugh thank you, you're a life saver

  13. jim_thompson5910
    • one year ago
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    you're welcome

  14. anonymous
    • one year ago
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    wait how'd you get \[\pi/4 \] to be 1

  15. jim_thompson5910
    • one year ago
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    tan of pi/4 is 1

  16. jim_thompson5910
    • one year ago
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    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)

  17. jim_thompson5910
    • one year ago
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    because of that and because tangent = sine/cosine, the two equal values divide to 1

  18. anonymous
    • one year ago
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    oooooooh okay, i get it now

  19. jim_thompson5910
    • one year ago
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    I'm glad it's making more sense

  20. anonymous
    • one year ago
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    Yeah I'm the worst at trigonometry lol

  21. jim_thompson5910
    • one year ago
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    I'm sure with more practice, you'll get better at it

  22. anonymous
    • one year ago
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    this is my third year learning this and I still haven't learned it :/

  23. jim_thompson5910
    • one year ago
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    then a different approach is needed

  24. anonymous
    • one year ago
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    yes, badly so for pi/3 , would it be radical 3 ? or do the 2's not cancel out ?

  25. jim_thompson5910
    • one year ago
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    the 2s will cancel leaving sqrt(3), correct

  26. anonymous
    • one year ago
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    Okay, I just wanted to make sure cause I've seen it where the 2's aren't being canceled out

  27. anonymous
    • one year ago
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    and since I'm doubling it, would it be \[2\sqrt{3}\] or ?

  28. jim_thompson5910
    • one year ago
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    I'd have to see the problem (where you didn't see the 2s cancel), but you should have this \[\Large \tan\left(\theta\right) = \frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\frac{\pi}{3}\right)}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}/2}{1/2}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\times\frac{2}{1}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{\cancel{2}}\times\frac{\cancel{2}}{1}\] \[\Large \tan\left(\frac{\pi}{3}\right) = \sqrt{3}\]

  29. jim_thompson5910
    • one year ago
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    yes, \[\Large 2\tan\left(\frac{\pi}{3}\right) = 2\sqrt{3}\]

  30. anonymous
    • one year ago
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    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

  31. jim_thompson5910
    • one year ago
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    hmm, strange

  32. anonymous
    • one year ago
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    but it just makes sense to cancel them out to me so I figured whoever made that table just forgot that step maybe?

  33. jim_thompson5910
    • one year ago
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    that's possible

  34. jim_thompson5910
    • one year ago
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    even teachers who write the problems and examples make typos

  35. anonymous
    • one year ago
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    I know many lol. But anyways, thank you so much

  36. jim_thompson5910
    • one year ago
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    sure thing

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