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lilsis76

  • 3 years ago

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

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  1. lilsis76
    • 3 years ago
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    @zepdrix

  2. Raja99
    • 3 years ago
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    120,360

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

  4. lilsis76
    • 3 years ago
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    haha okay so then hmmm

  5. lilsis76
    • 3 years ago
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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?

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

  7. anikay
    • 3 years ago
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    it should have 4 solutions right?

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

  9. Raja99
    • 3 years ago
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    yes!

  10. zepdrix
    • 3 years ago
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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

  11. anikay
    • 3 years ago
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    ^concur

  12. lilsis76
    • 3 years ago
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    lol ya, i got tired ofputting theata.

  13. Raja99
    • 3 years ago
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    30

  14. lilsis76
    • 3 years ago
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    okay is it 60 and 300 degrees?

  15. Raja99
    • 3 years ago
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    no tetha is 30

  16. zepdrix
    • 3 years ago
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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?

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

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

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

  20. zepdrix
    • 3 years ago
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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.

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

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

  23. anikay
    • 3 years ago
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    I think 120 is it.....

  24. zepdrix
    • 3 years ago
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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.

  25. lilsis76
    • 3 years ago
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    yes :) 1st and 4th

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

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

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

  29. anikay
    • 3 years ago
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    or am I failing?

  30. zepdrix
    • 3 years ago
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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 :)

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

  32. anikay
    • 3 years ago
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    With zepdrix, but you are right

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

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

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

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

  37. lilsis76
    • 3 years ago
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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

  38. anikay
    • 3 years ago
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    no, 5pi/6 = 150 degrees

  39. lilsis76
    • 3 years ago
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    haha shoot what am i doing wrong

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

  41. lilsis76
    • 3 years ago
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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???

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

  43. lilsis76
    • 3 years ago
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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?

  44. lilsis76
    • 3 years ago
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    @anikay

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

  46. zepdrix
    • 3 years ago
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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.

  47. anikay
    • 3 years ago
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    yup^

  48. zepdrix
    • 3 years ago
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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

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

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

  51. anikay
    • 3 years ago
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    and since we're going only to 360?

  52. anikay
    • 3 years ago
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    (radians are easier imo but degrees work k)

  53. lilsis76
    • 3 years ago
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    AH!!! im so lost haha

  54. zepdrix
    • 3 years ago
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    aw :D

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

  56. lilsis76
    • 3 years ago
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    lol,

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

  58. lilsis76
    • 3 years ago
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    @anikay

  59. anikay
    • 3 years ago
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    yes, and the 300

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

  61. anikay
    • 3 years ago
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    it's a reference angle of 60

  62. lilsis76
    • 3 years ago
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    yes it is a ref angle 60

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

  64. lilsis76
    • 3 years ago
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    right?! dang i think im slow

  65. anikay
    • 3 years ago
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    uh

  66. lilsis76
    • 3 years ago
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    haha did i do it right?!

  67. anikay
    • 3 years ago
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    yes

  68. lilsis76
    • 3 years ago
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    YAY!!!! > . < THANK YOU SO MUCH!!! ugh....

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

  70. phi
    • 3 years ago
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    sometimes sketching the curve is helpful |dw:1355239813847:dw|

  71. anikay
    • 3 years ago
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    agreed, but my calculator is dead xD

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