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Christos

  • 2 years ago

WHERE IS MY MISTAKE?!?!? Problem: Given that sinƟ = 2/3 and Π/2 < Ɵ < Π find the exact value of cosƟ My solution: cos^2(Ɵ) + sin^2(Ɵ) = 1 sin^2(Ɵ) = 1 - cos^2(Ɵ) 4/9=1- cos^2(Ɵ) -5/9 = -cos^2(Ɵ) 5/9 = cos^2(Ɵ) cos(Ɵ) = -sqrt(5/9) Where is my mistake till now?

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  1. satellite73
    • 2 years ago
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    for one thing, the square root of 9 is 3

  2. satellite73
    • 2 years ago
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    so if you were typing in an answer, it probably wanted it to look like \[\cos(\theta)=-\frac{\sqrt{5}}{3}\]

  3. satellite73
    • 2 years ago
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    other than that, it is all correct

  4. Christos
    • 2 years ago
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    @satellite73 So I didnt make any mistakes at all?

  5. geerky42
    • 2 years ago
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    No.

  6. Christos
    • 2 years ago
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    @satellite73 confirm to me please if all of my steps above were correct, and even if they had a mistake which line?

  7. babycry
    • 2 years ago
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    just draw a triangle and with 0 = 2 and h = 3.. then find a then do a/h to get cos theta

  8. Grazes
    • 2 years ago
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    |dw:1362625931832:dw|

  9. satellite73
    • 2 years ago
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    there is no mistake, although you should have \[\pm\sqrt{1-\left(\frac{2}{3}\right)^2}=\cos(\theta)\]

  10. Christos
    • 2 years ago
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    I should have used another fundamental identity?

  11. satellite73
    • 2 years ago
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    or if you write \[\frac{5}{9}=\cos^2(\theta)\] then \[\pm\frac{\sqrt{5}}{3}=\cos(\theta)\] the reason you know it is negative is because you are in quadrant 2

  12. Christos
    • 2 years ago
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    got it its the same just modified, meeh

  13. satellite73
    • 2 years ago
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    it is right, everything you did is right

  14. Christos
    • 2 years ago
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    I know why its negative yea

  15. Christos
    • 2 years ago
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    problem is that My solution is different from the one on the book

  16. satellite73
    • 2 years ago
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    so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9

  17. satellite73
    • 2 years ago
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    what did the book get?

  18. Christos
    • 2 years ago
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    They the solutions might be equal but, I sill found a different solution

  19. Christos
    • 2 years ago
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    5/9

  20. satellite73
    • 2 years ago
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    a different solution, or a different method

  21. Christos
    • 2 years ago
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    yea right..

  22. satellite73
    • 2 years ago
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    nothing wrong with your method answer is \(-\frac{\sqrt{5}}{3}\) for sure

  23. Christos
    • 2 years ago
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    Books solution: 5/9

  24. satellite73
    • 2 years ago
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    no that is \(\cos^2(\theta)\)

  25. satellite73
    • 2 years ago
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    or else the book made a mistake it happens in any case you are right for sure, so don't fret about it

  26. Christos
    • 2 years ago
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    what do you mean "no that is cos2(θ)" ?

  27. satellite73
    • 2 years ago
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    \[\cos(\theta)=-\frac{\sqrt{5}}{3}\] \[\cos^2(\theta)=\frac{5}{9}\]

  28. Christos
    • 2 years ago
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    hmmmmm

  29. Christos
    • 2 years ago
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    Is there any other method to approche the situation, like another identity to use for the specidif prob

  30. Christos
    • 2 years ago
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    I AM SORRY the answer in my book was: -sqrt(5)/3 !!!!!

  31. babycry
    • 2 years ago
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    |dw:1362626751880:dw|

  32. Christos
    • 2 years ago
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    So my final outcome is - sqrt(5)/sqrt3 HOW DO I PROCEED?

  33. Christos
    • 2 years ago
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    @satellite73

  34. Christos
    • 2 years ago
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    @Hero

  35. Christos
    • 2 years ago
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    @Mertsj

  36. Christos
    • 2 years ago
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    SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE

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