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anonymous

  • one year ago

if sin theta equals -5/13 pi is less than theta less than 3 pi/2 find cos theta over 2 This is just all over the place

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  1. anonymous
    • one year ago
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    If \(\sin \theta = -\frac{ 5 }{ 13 }, \pi<\theta<\frac{ 3\pi }{ 2 }\), find \(\cos \frac{ \theta }{ 2 }\). this?

  2. anonymous
    • one year ago
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    haha yes!

  3. anonymous
    • one year ago
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    you need to use the half angle identity \[\cos \theta = \pm \sqrt{\frac{ 1+\cos \theta }{ 2}}\] which means you need to find cos Θ.

  4. anonymous
    • one year ago
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    Where are you suppose to use the sin theta part then?

  5. anonymous
    • one year ago
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    Θ is in the 3rd quadrant so cos Θ is negative, and you can use the pythagorean theorem/triples to find it

  6. anonymous
    • one year ago
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    Right so its 5 12 13 triangle what would you use for the cos theta part?

  7. anonymous
    • one year ago
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    yes

  8. anonymous
    • one year ago
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    so cos Θ would be -12/13

  9. anonymous
    • one year ago
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    make sense?

  10. anonymous
    • one year ago
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    So then you would just solve after?

  11. anonymous
    • one year ago
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    right

  12. anonymous
    • one year ago
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    Alright lets see how this works working it out then I might show you the work to see if its correct lol

  13. anonymous
    • one year ago
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    @peachpi Like this?

  14. anonymous
    • one year ago
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    I can't really see if the 12/13 is negative. If it is then you're right and you just have to simplify it

  15. anonymous
    • one year ago
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    Alright yeah its negative sorry its hard to tell but we got sqrt of 1 over 26?

  16. anonymous
    • one year ago
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    that's what I got. Then since Θ is in the third quadrant, Θ/2 is in the second where cos is negative so got with -√(1/26)

  17. anonymous
    • one year ago
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    or -(√26)/26 if you have to rationalize

  18. anonymous
    • one year ago
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    but I don't think either of them are right becauase the answer has to be greater then pi and less then 3 pi over 2?

  19. anonymous
    • one year ago
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    that's a restriction on Θ. That's how we know Θ is in the 3rd quadrant.|dw:1436551969316:dw|

  20. anonymous
    • one year ago
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    the question is asking for cos (Θ/2), not Θ itself

  21. anonymous
    • one year ago
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    The answer is simple, A true saiyan sprinkles when he tinkles.

  22. anonymous
    • one year ago
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    Wait so whats the answer then? im so confused lmaoo

  23. anonymous
    • one year ago
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    I just said it

  24. anonymous
    • one year ago
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    cos (Θ/2) = -√(1/26)

  25. anonymous
    • one year ago
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    Is there a way to check the answer itself?

  26. anonymous
    • one year ago
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    try wolframalpha.com not sure how you'd have to word it though

  27. anonymous
    • one year ago
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    But are you sure your right? with the answer and everything?

  28. anonymous
    • one year ago
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    yes

  29. anonymous
    • one year ago
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    Alright I have an exam coming up which is why I am asking these questins XD haha thank you!

  30. anonymous
    • one year ago
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    you're welcome

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