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anonymous

  • one year ago

If tan theta =12/5 and cos theta =-5/13, then what is sin theta?

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  1. anonymous
    • one year ago
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    @peachpi

  2. Michele_Laino
    • one year ago
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    hint: \[\tan \theta = \frac{{\sin \theta }}{{\cos \theta }}\]

  3. anonymous
    • one year ago
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    i am confused

  4. anonymous
    • one year ago
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    @Michele_Laino totally missed that. Much simpler than what I was going to do

  5. anonymous
    • one year ago
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    how do i go on from there

  6. anonymous
    • one year ago
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    what @Michele_Laino has posted is an identity for tan. From here you plug in your numbers and solve for sin Θ

  7. Michele_Laino
    • one year ago
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    ok! please continue @peachpi

  8. anonymous
    • one year ago
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    the answer i got is 12/13

  9. anonymous
    • one year ago
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    im not sure what i did, is that correct

  10. anonymous
    • one year ago
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    you should have gotten a negative number

  11. UsukiDoll
    • one year ago
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    you're missing a negative sign.

  12. anonymous
    • one year ago
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    so the answer would be -12/13???

  13. anonymous
    • one year ago
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    yes

  14. anonymous
    • one year ago
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    i just did the question again and got -5/13..... i am overthinking the problem i think

  15. anonymous
    • one year ago
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    so the answer is -12/13

  16. anonymous
    • one year ago
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    |dw:1436185957944:dw|

  17. UsukiDoll
    • one year ago
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    \[\tan(\theta)\cos(\theta) = \sin(\theta) \] since we are given 12/5 for tangent and -5/13 for cosine \[\frac{12}{5}(\frac{-5}{13}) = \sin(\theta) \] the 5's cancel and you are left with -12/13

  18. UsukiDoll
    • one year ago
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    wow this is the first time I've done like this to be honest xD

  19. anonymous
    • one year ago
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    thank you guys!!!!!!

  20. anonymous
    • one year ago
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    me too. I usually draw it and use the quadrants

  21. anonymous
    • one year ago
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    you're welcome

  22. UsukiDoll
    • one year ago
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    same... since sin was negative and cos was negative, I'm assuming that we were in quadrant 3 because tangent is positive.

  23. anonymous
    • one year ago
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    yes. I was dutifully drawing a picture when michele came in and blew my mind xD

  24. UsukiDoll
    • one year ago
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    hmmm the triangle method would've worked too.. because tangent = opposite/adjacent = 12/5 and cosine = adjacent/hypotenuse =- 5/13 |dw:1436186175987:dw| except we have to respect the fact that since cosine is negative we are placed in one of the four quadrants.

  25. UsukiDoll
    • one year ago
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    yeah I remember have those problems with the triangles like this and the textbook was like one of them is negative so which quadrant are we

  26. UsukiDoll
    • one year ago
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    sorry my typing not working tonight xD but quadrant three is 180 degrees-270 degrees and only tangent is positive.

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