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UnbelievableDreams

  • one year ago

Confusing math question

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  1. UnbelievableDreams
    • one year ago
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    Find all values of theta in the interval [0, 360] that have the given function valve. cos theta = -1/2

  2. Astrophysics
    • one year ago
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    Do you know your special triangles, 30-45-60

  3. UnbelievableDreams
    • one year ago
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    No, I think.

  4. Astrophysics
    • one year ago
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    |dw:1437017727352:dw|

  5. Astrophysics
    • one year ago
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    These are the special triangles, you should try to remember them, so we're given \[\cos \theta = - \frac{ 1 }{ 2 } = \frac{ adj }{ hyp }\] so what is it

  6. Astrophysics
    • one year ago
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    Once we figure out the triangle, we can use the following information to find the quadrants it is in.

  7. UnbelievableDreams
    • one year ago
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    It is 60

  8. Astrophysics
    • one year ago
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    So for now, jut figure out \[\cos \theta = \frac{ 1 }{ 2 }\]

  9. Astrophysics
    • one year ago
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    Yeah :)

  10. Astrophysics
    • one year ago
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    Now we can figure out, where in the unit circle it would be negative, if you remember this thing called "CAST" |dw:1437018190660:dw| this shows where the trig ratios are positive

  11. Astrophysics
    • one year ago
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    So if you drew out triangles, you would notice for example in quadrant 4, y is negative but x is positive and also r (where x = adjacent, y = opposite, r = hypotenuse) and in quadrant 1 they are all positive, so quadrant 4 means costheta is positive, A means all positive, s means sin theta is positive, and t means tangent is positive.

  12. Astrophysics
    • one year ago
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    Sort of getting it?

  13. Astrophysics
    • one year ago
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    |dw:1437018375815:dw|

  14. Astrophysics
    • one year ago
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    So where in here would cos theta be negative?

  15. UnbelievableDreams
    • one year ago
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    IV?

  16. UnbelievableDreams
    • one year ago
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    @Astrophysics

  17. Astrophysics
    • one year ago
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    Well the quadrants here mean they are all positive in the certain area, so where it shows C that means it's positive, A means all of the ratios here are positive there, so for it to be negative it must be in Q2 and Q3 right?

  18. UnbelievableDreams
    • one year ago
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    Yes

  19. Astrophysics
    • one year ago
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    So for quadrant 2 we have \[Q_2: 180 - 60 = ...\]and for quadrant 3 we have \[Q_3: 180 + 60 = ...\]

  20. UnbelievableDreams
    • one year ago
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    120, 240

  21. Astrophysics
    • one year ago
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    Yup, those are your values then in the interval [0,360] :)

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