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amsterdam11

  • 2 years ago

Could someone please help me with sqrt(3) tan2x=0

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  1. lgbasallote
    • 2 years ago
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    what do you want to do with it?

  2. amsterdam11
    • 2 years ago
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    solve for x

  3. lgbasallote
    • 2 years ago
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    \[\sqrt 3 \tan (2x) = 0\] first step divide both sides by \(\sqrt{3}\) what do you get?

  4. y2o2
    • 2 years ago
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    x = 0 or x = 180

  5. amsterdam11
    • 2 years ago
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    so tan2x=-1/sqrt(3)

  6. lgbasallote
    • 2 years ago
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    nope. \[\tan (2x) =\frac {0}{\sqrt3}\] now simplify this

  7. amsterdam11
    • 2 years ago
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    oh dear! sorry i didnt realise! The question is sqrt(3) tan2x+1=0

  8. amsterdam11
    • 2 years ago
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    sorry!

  9. lgbasallote
    • 2 years ago
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    haha..then you're right \[\tan(2x) =-\frac{1}{\sqrt 3}\]

  10. lgbasallote
    • 2 years ago
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    now second step. take the arctangent of both sides

  11. amsterdam11
    • 2 years ago
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    ok so pi/6?

  12. lgbasallote
    • 2 years ago
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    remember that negative sign...and it's not yet over

  13. amsterdam11
    • 2 years ago
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    how does the negative affect it?

  14. lgbasallote
    • 2 years ago
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    well it doesnt affect that much

  15. amsterdam11
    • 2 years ago
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    how do you mean?

  16. lgbasallote
    • 2 years ago
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    |dw:1342705038280:dw|

  17. amsterdam11
    • 2 years ago
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    oh ok so when you say take the arctangent, where do you go from there?

  18. lgbasallote
    • 2 years ago
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    so \[2x = -\frac{\pi}{6}\] now you divide both sides by 2

  19. amsterdam11
    • 2 years ago
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    ok so x= =pi/12

  20. amsterdam11
    • 2 years ago
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    -pi/12

  21. lgbasallote
    • 2 years ago
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    yup

  22. amsterdam11
    • 2 years ago
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    is this one of the answers?

  23. lgbasallote
    • 2 years ago
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    what do you mean?

  24. amsterdam11
    • 2 years ago
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    well there are 4 values for x right?

  25. amsterdam11
    • 2 years ago
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    because there was a 2 between the tan and the x, which compresses the tan graph

  26. lgbasallote
    • 2 years ago
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    i cant remember that part...is it adding \(\pi\) or \(2\pi\)

  27. lgbasallote
    • 2 years ago
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    what do you mean 2 between tan and x..tan (2x)?

  28. amsterdam11
    • 2 years ago
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    yeah, thats what i meant tan2x

  29. amsterdam11
    • 2 years ago
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    i think its add pi

  30. lgbasallote
    • 2 years ago
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    im not sure about this part so im gonna ask @amistre64 for some assistance. please come sir.

  31. amsterdam11
    • 2 years ago
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    Thank you for your help so far!!

  32. amsterdam11
    • 2 years ago
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    what does amistre64 say?

  33. lgbasallote
    • 2 years ago
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    i dont think he's coming yet...i tried tagging him to come here...

  34. lgbasallote
    • 2 years ago
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    let me call a different one..he might be afk

  35. amsterdam11
    • 2 years ago
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    Thank you :)

  36. lgbasallote
    • 2 years ago
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    @apoorvk pls help

  37. vamgadu
    • 2 years ago
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    just add pi to the solution and it wont matter.

  38. amsterdam11
    • 2 years ago
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    so 11pi/12?

  39. vamgadu
    • 2 years ago
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    yep i do think its another answer.

  40. lgbasallote
    • 2 years ago
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    thanks @vamgadu you saved me there heh

  41. amsterdam11
    • 2 years ago
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    yes thank you! :)

  42. vamgadu
    • 2 years ago
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    its my pleasure @lgbasallote

  43. amsterdam11
    • 2 years ago
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    however, in the back of my text book the answers are 5pi/12 11pi/12 17pi/12 and 23pi/12

  44. amsterdam11
    • 2 years ago
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    and im wondering how my magic maths textbook got there

  45. amsterdam11
    • 2 years ago
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    so we are going good with the 11pi/12 :D

  46. amsterdam11
    • 2 years ago
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    and if pi is added again, we get 23pi/12 which is also good!

  47. lgbasallote
    • 2 years ago
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    you're doing right. so is there a further problem?

  48. amsterdam11
    • 2 years ago
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    well there are sposed to be 4 answers

  49. lgbasallote
    • 2 years ago
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    then you add pi again

  50. amsterdam11
    • 2 years ago
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    i have 2 :)

  51. lgbasallote
    • 2 years ago
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    2?

  52. vamgadu
    • 2 years ago
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    subtract a pi, if want int he interval, [-2pi,2pi]

  53. amsterdam11
    • 2 years ago
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    well i have 11pi/12 and 23pi/12

  54. vamgadu
    • 2 years ago
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    -pi/12 and -13pi/12

  55. amsterdam11
    • 2 years ago
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    so 11pi/12-pi?

  56. lgbasallote
    • 2 years ago
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    -pi/12 - pi

  57. lgbasallote
    • 2 years ago
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    11pi/12 - pi is -pi/12 (bringing you back to the orig thingy)

  58. amsterdam11
    • 2 years ago
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    thats not one of the answers :?

  59. phi
    • 2 years ago
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    You started with 2x= -pi/6 if we call 2x theta, we have 2 solutions: |dw:1342706814544:dw| and x is 5pi/12 and 11pi/12 now add pi to each value to get the other 2 solutions or , noting that 2x+pi divided by 2 is x+pi/2 , add multiplies of pi/2 to get all four solutions starting with -pi/12 (which is 11pi/12 in the interval [0, 2pi] )

  60. amsterdam11
    • 2 years ago
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    can this be done on a tan graph?

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