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anonymous

  • one year ago

Will Medal! If 2tanx/ (1-tan^2x) = 1, then x can equal ____. Check all that apply. A) x=5pi/8 + npi B) x=pi/8 + npi C) x=3pi/8 + npi D) x=7pi/8 + npi

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  1. anonymous
    • one year ago
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    I think it is A and B. But this is me taking a guess. I am terrible at trig. Sorry

  2. welshfella
    • one year ago
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    well first cross multiply to give 2 tanx = 1 - tan^2 x now rearrange this quadratic: tan^2 x + 2tanx - 1 = 0 can you factor this?

  3. anonymous
    • one year ago
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    Yes. I am thinking you factor to get tan^2x = -2tan(x)+1?

  4. welshfella
    • one year ago
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    no factor as you would any quadratic like x^2 + 3x + 2 = (x + 1)(x + 2)

  5. welshfella
    • one year ago
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    oh sorry - on second look this will not factor so you need to use the quadratic formula

  6. anonymous
    • one year ago
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    So would a = tan^2x b =2tanx and c=-1?

  7. welshfella
    • one year ago
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    no a , b and c are the coefficients of tan^2x and tan x so a = 1 , b = 2 and c = -1

  8. anonymous
    • one year ago
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    So x = +/- sqrt (2) in the end right?

  9. anonymous
    • one year ago
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    *-1 +/- sqrt(2)

  10. welshfella
    • one year ago
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    -2 +/- sqrt(4 - 4*1*-1) / 2 = -2 +/- sqrt8 / 2 = (-2 +/- 2 * sqrt2 )/ 2 = -1 +/- sqrt2 yep

  11. anonymous
    • one year ago
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    Awesome! So now do I just plug in this to my original equation?

  12. welshfella
    • one year ago
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    well they have the answer options in terms of pi so convert everything to decimals so for example -1 + sqrt2 = 0.4142 so find the angle in radians which is the tangent of 0.4142 and see if one of the options gives the the same angle

  13. welshfella
    • one year ago
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    eg angle with tangent 0.4142 = 0.39269 radians now check if pi/8 gives the same value

  14. anonymous
    • one year ago
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    Yes it does!

  15. anonymous
    • one year ago
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    So I'm assuming that is one

  16. welshfella
    • one year ago
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    ok so thats one result pi/8 + npi

  17. welshfella
    • one year ago
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    now try the other value for tan x

  18. anonymous
    • one year ago
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    -1 - sqrt 2 = -2.4142 degrees right?

  19. welshfella
    • one year ago
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    yes

  20. anonymous
    • one year ago
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    Ok so then the radians of -2.4142 is -0.042135

  21. anonymous
    • one year ago
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    I don't think I did it right

  22. welshfella
    • one year ago
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    no the -2.4142 is the value of tan x so you need tan-1(-2.4242)

  23. anonymous
    • one year ago
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    Oh ok that would make it -1.1781 which is basically the same as 3pi/8 right?

  24. anonymous
    • one year ago
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    So the answers would be pi/8 + npi and 3pi/8 + npi

  25. welshfella
    • one year ago
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    yes

  26. anonymous
    • one year ago
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    Great!! Thank you for taking the time to help me! I feel I really understand now! Thank you!

  27. anonymous
    • one year ago
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    Weird... I hit the sumit button and it told me it was 5pi/8 instead of 3/pi/8

  28. welshfella
    • one year ago
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    lets check that out

  29. myininaya
    • one year ago
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    \[\frac{2tanx}{1-\tan^2x} = 1 \\ \tan(2x)=1\]

  30. myininaya
    • one year ago
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    \[\tan(u)=1 \text{ when } u=?\]

  31. welshfella
    • one year ago
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    ahh i forgot that identity !

  32. welshfella
    • one year ago
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    u = pi/4 of course and x will be pi/8

  33. welshfella
    • one year ago
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    much easier that way lol!

  34. myininaya
    • one year ago
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    and there is also the u=5pi/4 so yep x=5pi/8

  35. welshfella
    • one year ago
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    yes

  36. welshfella
    • one year ago
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    -1.1781 is an incorrect result then? - an extraneous result right?

  37. myininaya
    • one year ago
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    does give tan(2x) approx 1 what number are you approximating ?

  38. myininaya
    • one year ago
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    oh -3pi/8 is what you are approximating

  39. welshfella
    • one year ago
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    sorry I dont follow you -yes

  40. myininaya
    • one year ago
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    that gives 1

  41. myininaya
    • one year ago
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    when you plug in

  42. welshfella
    • one year ago
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    and -3pi/8 is equivalent to 5pi/8

  43. myininaya
    • one year ago
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    is that not included in the solution: \[\frac{5\pi}{8}+n \pi \\ \text{ if } n=-1 \text{ then } \frac{5\pi}{8}-\pi=\frac{-3\pi}{8}\] so I'm not sure why you say it is extraneous

  44. welshfella
    • one year ago
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    no - i was wrong its not extraneous

  45. welshfella
    • one year ago
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    still i think lehmad learned something along the line...

  46. anonymous
    • one year ago
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    Yes I learned a lot! Thank you guys for the help.

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