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lilsis76

Determine all of the solutions in the interval 0< Theta < 360. cos(Q/2) = 1/2 Q is theta

  • one year ago
  • one year ago

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  1. lilsis76
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    @zepdrix

    • one year ago
  2. Raja99
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    120,360

    • one year ago
  3. anikay
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    oh my, beaten to the punch gj

    • one year ago
  4. lilsis76
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    haha okay so then hmmm

    • one year ago
  5. lilsis76
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    how would that be? @zepdrix i dont get it. i see cos Q/2 that would mean cos = 1/2 right? and if its positive it would be in the 1st and 4th Quadrant?

    • one year ago
  6. anikay
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    well, now that I think about it, I think raja might be wrong

    • one year ago
  7. anikay
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    it should have 4 solutions right?

    • one year ago
  8. lilsis76
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    im not sure, it just says to determine all solutions in the interval 0-->360

    • one year ago
  9. Raja99
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    yes!

    • one year ago
  10. zepdrix
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    Using Q? Oooo I like that :) I'm always having trouble finding a suitable letter for theta in text, that works quite well XD

    • one year ago
  11. anikay
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    ^concur

    • one year ago
  12. lilsis76
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    lol ya, i got tired ofputting theata.

    • one year ago
  13. Raja99
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    30

    • one year ago
  14. lilsis76
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    okay is it 60 and 300 degrees?

    • one year ago
  15. Raja99
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    no tetha is 30

    • one year ago
  16. zepdrix
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    \[\large \cos(\theta/2)=\frac{1}{2}\]We need to solve for theta, which involves a little more than just finding a special angle. If it helps, think of the ENTIRE inside of cosine as an angle, like this,\[\large \cos(\phi)=\frac{1}{2}\]Where is phi =1/2? Which special angles?

    • one year ago
  17. anikay
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    look, as I solve it, it's \[\theta=2\cos^{-1} (1/2)\]

    • one year ago
  18. anikay
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    the thing is, that only gives you 120. but it's a good starting point

    • one year ago
  19. lilsis76
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    mmmmm... okay, well first. special angles is like 45-45-90, and 30-60-90, right?

    • one year ago
  20. zepdrix
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    The special angles are 0,30, 45, 60, 90 In radians 0, pi/6, pi/4, pi/3, pi/2 and so on... Remember those? :) We're not talking about special triangles :D Special angles on the unit circle.

    • one year ago
  21. lilsis76
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    oh....okay i gotcha now on special angles. lol im totaly flipped around in this class

    • one year ago
  22. lilsis76
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    okay then so..cosQ/2 = 1/2 right? so cos would be a positive

    • one year ago
  23. anikay
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    I think 120 is it.....

    • one year ago
  24. zepdrix
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    yes the cosine is producing a positive value, so we're concerned with angles in the 1st and 4th quadrant right? :O Cuz that's where cosine is positive.

    • one year ago
  25. lilsis76
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    yes :) 1st and 4th

    • one year ago
  26. anikay
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    so, if we find the reference angle, then what would the two angles be?

    • one year ago
  27. lilsis76
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    mmm....pi/3 and 5pi/6?

    • one year ago
  28. anikay
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    yes to the first, the last, not so much, that's in the second quadrant

    • one year ago
  29. anikay
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    or am I failing?

    • one year ago
  30. zepdrix
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    lol :) They should both either be /6 or /3 :D you should get similar angles in that sense. Also, the domain of theta was given to us in DEGREES. let's try to keep it in degrees :)

    • one year ago
  31. lilsis76
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    oh. haha i mean 5pi/3

    • one year ago
  32. anikay
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    With zepdrix, but you are right

    • one year ago
  33. lilsis76
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    so the second answer would be 5pi/3?

    • one year ago
  34. anikay
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    but, the problem is, we need that angle to be doubled to match our equation of theta/2

    • one year ago
  35. lilsis76
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    hmmm...ok okkay, so doubled from pi/3, so pi/3 and 5pi/6?

    • one year ago
  36. anikay
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    uh, lets throw this back to degrees shall we? pi/3 = 60 and 5pi/3 = 300

    • one year ago
  37. lilsis76
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    DANG! haha okay, so first we have 60 and u said to double it, so that would be 120, 120 would be.....that 5pi/6

    • one year ago
  38. anikay
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    no, 5pi/6 = 150 degrees

    • one year ago
  39. lilsis76
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    haha shoot what am i doing wrong

    • one year ago
  40. anikay
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    here's a tip. every pi/6 = 30 degrees

    • one year ago
  41. lilsis76
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    pi/6 pi/4 pi/3 pi/2 4pi/6div by 2 = 2pi/3 OH!.....haha okay so pi/3 and 2 pi/3???

    • one year ago
  42. anikay
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    just plug those into your original equation and see what you get :P

    • one year ago
  43. lilsis76
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    i dont have an equatioN haha says determine all of the solutions in the interval 0< Q<360 cos(Q/2) = 1/2 so the answers would be pi/3 and 2pi/3? right?

    • one year ago
  44. lilsis76
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    @anikay

    • one year ago
  45. lilsis76
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    @zepdrix is it pi/3 and 2pi/3?

    • one year ago
  46. zepdrix
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    If the problem had been,\[\large \cos\left(\theta\right)=\frac{1}{2}\]We would have concluded that,\[\large \theta=\quad 60^o,\quad 300^o\] But our problem involved Q/2, not Q. Giving us,\[\large \cos\left(\frac{\theta}{2}\right)=\frac{1}{2}\] \[\frac{\theta}{2}=\quad 60^o,\quad 300^o\] From here, if we multiply both sides by 2, we can solve for Q.

    • one year ago
  47. anikay
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    yup^

    • one year ago
  48. zepdrix
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    I'm a little confused why you're messing with the radians :C They're a little more confusing to work with. The domain of Q was GIVEN to us in DEGREES. So let's work in degrees! :D

    • one year ago
  49. lilsis76
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    AH! so i was right?! the 60 and 300?!

    • one year ago
  50. zepdrix
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    \[\large \theta=\quad 120^o, \quad 600^o\]

    • one year ago
  51. anikay
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    and since we're going only to 360?

    • one year ago
  52. anikay
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    (radians are easier imo but degrees work k)

    • one year ago
  53. lilsis76
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    AH!!! im so lost haha

    • one year ago
  54. zepdrix
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    aw :D

    • one year ago
  55. anikay
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    its almost like you're my lilsis or somethin xD

    • one year ago
  56. lilsis76
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    lol,

    • one year ago
  57. lilsis76
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    okay so i get the 1/2 and that is in the first quad giving me 60 degrees right?

    • one year ago
  58. lilsis76
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    @anikay

    • one year ago
  59. anikay
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    yes, and the 300

    • one year ago
  60. lilsis76
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    okay, how can i figure out the 300?!

    • one year ago
  61. anikay
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    it's a reference angle of 60

    • one year ago
  62. lilsis76
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    yes it is a ref angle 60

    • one year ago
  63. lilsis76
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    WAIT!!! 300 cuz its cos 1.2, sin - sqrt3 /2 ?!

    • one year ago
  64. lilsis76
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    right?! dang i think im slow

    • one year ago
  65. anikay
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    uh

    • one year ago
  66. lilsis76
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    haha did i do it right?!

    • one year ago
  67. anikay
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    yes

    • one year ago
  68. lilsis76
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    YAY!!!! > . < THANK YOU SO MUCH!!! ugh....

    • one year ago
  69. anikay
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    however, you have to double those and since you only go to 360, 120 is your only answer

    • one year ago
  70. phi
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    sometimes sketching the curve is helpful |dw:1355239813847:dw|

    • one year ago
  71. anikay
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    agreed, but my calculator is dead xD

    • one year ago
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