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ygarcia

  • 2 years ago

Find COS 23pi/6?

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  1. nelsonjedi
    • 2 years ago
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    Do you have a calculator?

  2. ygarcia
    • 2 years ago
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    no

  3. Abiilovee911
    • 2 years ago
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    π=180∘

  4. ygarcia
    • 2 years ago
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    so I replace pi with 180?

  5. Abiilovee911
    • 2 years ago
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    yes

  6. ygarcia
    • 2 years ago
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    so it'd be 23*pi divided by 6?

  7. Abiilovee911
    • 2 years ago
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    exactly (:

  8. ygarcia
    • 2 years ago
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    thanks :)

  9. Abiilovee911
    • 2 years ago
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    welcome (:

  10. ygarcia
    • 2 years ago
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    Is 12.03 Right?

  11. RolyPoly
    • 2 years ago
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    cosine of a value cannot be larger than 1...

  12. ygarcia
    • 2 years ago
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    can you please explain?

  13. RolyPoly
    • 2 years ago
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    See the graph of cosine:|dw:1389756073553:dw|

  14. ygarcia
    • 2 years ago
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    yes

  15. RolyPoly
    • 2 years ago
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    Maximum of a y=cos x function is 1. Minimum of a y=cosx function is -1

  16. ygarcia
    • 2 years ago
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    so do I need to graph this?

  17. nelsonjedi
    • 2 years ago
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    |dw:1389756066410:dw|

  18. RolyPoly
    • 2 years ago
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    So, you cannot have COS 23pi/6 = 12.03

  19. RolyPoly
    • 2 years ago
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    \[\cos\frac{23\pi}{6} = \cos(3(2\pi) + \frac{5\pi}{6}) = \cos\frac{5\pi}{6} = ...?\]

  20. nelsonjedi
    • 2 years ago
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    Using the attached drawing where does 23/pi fall?

  21. Lethal
    • 2 years ago
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    Okay sir's let me tell you that. Cos23pi/6 -2pi will give you the same answer

  22. ygarcia
    • 2 years ago
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    idk where 23/pi falls

  23. Lethal
    • 2 years ago
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    Subtract 2pi from it

  24. Lethal
    • 2 years ago
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    The reason you don't know where it falls is becomes you have to do more than one revolution around the circle

  25. ygarcia
    • 2 years ago
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    so i subtract 2pi fom 6?

  26. nelsonjedi
    • 2 years ago
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    2pi = 12pi/6..So 23pi/6-12pi/6 = 11pi/6

  27. Lethal
    • 2 years ago
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    Okay good.

  28. nelsonjedi
    • 2 years ago
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    Are you familiar with the unit circle in trigonometry?

  29. Lethal
    • 2 years ago
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    Now if radians are bothering you we can convert it to degrees.

  30. ygarcia
    • 2 years ago
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    do i need like a specific calculator for this?

  31. ygarcia
    • 2 years ago
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    yes Please

  32. Lethal
    • 2 years ago
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    You could plug this into your calculator, but if this comes up on a test and you can't use one, you will be screwed.

  33. Lethal
    • 2 years ago
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    11pi/6*180/pi

  34. ygarcia
    • 2 years ago
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    Can you explain how to do it manually?

  35. Lethal
    • 2 years ago
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    That gives us 330 degrees

  36. Lethal
    • 2 years ago
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    Do you know where that is on the unit circle?

  37. Lethal
    • 2 years ago
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    hint: It's in quadrant IV

  38. ygarcia
    • 2 years ago
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    yes

  39. Lethal
    • 2 years ago
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    Okay. tell me the coordinates for it.

  40. ygarcia
    • 2 years ago
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    sqrt 2/2, -sqrt 2/2

  41. Lethal
    • 2 years ago
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    Not quite.

  42. Lethal
    • 2 years ago
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    That would be 315 degrees.

  43. ygarcia
    • 2 years ago
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    ummm sqrt 3/2 , -1/2

  44. Lethal
    • 2 years ago
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    yes. sqrt(3)/2, -1/2

  45. Lethal
    • 2 years ago
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    Okay. You should know that Cosx= x

  46. Lethal
    • 2 years ago
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    So what is the value for Cos330?

  47. ygarcia
    • 2 years ago
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    I got -.991...

  48. Lethal
    • 2 years ago
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    Keep this exact. You just gave me the coordinates. and I just told you CosƟ=x

  49. Lethal
    • 2 years ago
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    so what is the exact answer?

  50. Lethal
    • 2 years ago
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    hint: (x,y)

  51. Lethal
    • 2 years ago
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    Use the coordinates you gave me.

  52. ygarcia
    • 2 years ago
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    sqrt 3/2 , -1/2

  53. Lethal
    • 2 years ago
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    Yes and I told you cosƟ=x so what is cos330?

  54. ygarcia
    • 2 years ago
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    I don't get it /.\ I'm sorry

  55. ygarcia
    • 2 years ago
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    when I plug in Cos330 it gives me the decimal I gave you

  56. Lethal
    • 2 years ago
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    |dw:1389757103607:dw|

  57. Lethal
    • 2 years ago
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    Okay also cosƟ=A/H This is the unit circle and the hypotenuse will always be one so basically cosƟ=H what is Cos330?

  58. Lethal
    • 2 years ago
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    ygarcia what calculator are you using btw?

  59. ygarcia
    • 2 years ago
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    I don't have a calculator

  60. Lethal
    • 2 years ago
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    Okay. Well just finish it. Cos330=A. What is A in that triangle? A for adjacent to theta.

  61. ygarcia
    • 2 years ago
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    -1/2?

  62. Lethal
    • 2 years ago
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    |dw:1389757356882:dw|

  63. Lethal
    • 2 years ago
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    No. Adjacent means next to. So what is next to theta that isn't the hypotenuse. -1/2 is opposite.

  64. ygarcia
    • 2 years ago
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    sqrt 3/2

  65. Lethal
    • 2 years ago
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    There you go.

  66. ygarcia
    • 2 years ago
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    so the solution is sqrt 3/2?

  67. Lethal
    • 2 years ago
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    cos330=Sqrt(3)/2

  68. Lethal
    • 2 years ago
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    Yes

  69. Lethal
    • 2 years ago
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    Now let's see if you learned anything. Tell me the sin330 if you know that sinƟ=y

  70. ygarcia
    • 2 years ago
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    -1/2

  71. Lethal
    • 2 years ago
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    Very good. Just use the coordinates you gave me for that degree value. (sqrt(3)/2, -1/2) (x,y) SinƟ=y and the y value for 330 is -1/2 so that's the answer.

  72. ygarcia
    • 2 years ago
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    So Cos= x value and Sin= y value?

  73. ygarcia
    • 2 years ago
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    In reference to the circle

  74. Lethal
    • 2 years ago
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    Yeah. Because in the unit circle the radius is one, that's why it's called a unit circle, one unit. Anytime you have something over 1 It's just whatever the numerator is.

  75. ygarcia
    • 2 years ago
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    Okay, Thanks SO MUCH!!!! I don't fully get it yet but what you explained to me helped A LOT :)

  76. Lethal
    • 2 years ago
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    You're welcome.

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