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anonymous

  • 4 years ago

Solve 1 = cot^2(x) = 8sinx, for 0(lesser-than-or-equal-to) x (lesser-than-or-equal-to) 360 degrees??

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  1. anonymous
    • 4 years ago
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    r u sure u have correct question? The two '=' signs?

  2. anonymous
    • 4 years ago
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    sorry, 1+ cot^2.....

  3. anonymous
    • 4 years ago
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    my bad. didn't press shift.

  4. anonymous
    • 4 years ago
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    ahh u could try replacing cot^2x with cosec^2x - 1 = 1/sin^2x + 1

  5. anonymous
    • 4 years ago
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    but that would be 1 + coesc^2x - 1, which would be cosec^x.

  6. anonymous
    • 4 years ago
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    hmm lets try this: 1 + ( 1 - sin^2x) = 8 sinx ---------- sin^2x sin^2x + 1 - sin^2x = 8 sin^3 x sin^3 x = 1/8 s in x = +/- 1/2

  7. anonymous
    • 4 years ago
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    x = 30, 150, 210, 330 degrees

  8. anonymous
    • 4 years ago
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    how did you get that?? \[1 + \cot^2x = 8sinx\] so \[cosec^2x = 8sinx\] now what??

  9. anonymous
    • 4 years ago
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    cosec^2 x = 1 / sin^2 x

  10. anonymous
    • 4 years ago
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    yes. so?

  11. anonymous
    • 4 years ago
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    you replace cot^2x by cosec^2 x - 1 because cosec^2x = 1 + cot^ 2 x

  12. anonymous
    • 4 years ago
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    but you can replace 1 = cot^2x by cosec^2x straight away!!

  13. anonymous
    • 4 years ago
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    *1 + cot^2x

  14. anonymous
    • 4 years ago
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    yea right - i didnt see the obvious! - but my method comes out with the same answer. your way is better though! they both come to 1 / sin^2x = 8 sinx cross multiply: 8 sin^3 x = 1 sin^3 x = 1/8 sin x = 1/2 or -1/2

  15. anonymous
    • 4 years ago
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    ohhh. cool. i didn't know how to simplify it :P

  16. anonymous
    • 4 years ago
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    but it can't be -0.5, though, can it??

  17. anonymous
    • 4 years ago
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    hold on - sorry - i-m prone to error today the cube root of 1/8 is 1/2 only so x = 30, 150 only

  18. anonymous
    • 4 years ago
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    i think tahs correct now lol!

  19. anonymous
    • 4 years ago
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    it's okayy, i have these weird days too :P

  20. anonymous
    • 4 years ago
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    can you help me with another question??

  21. anonymous
    • 4 years ago
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    ok

  22. anonymous
    • 4 years ago
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    http://openstudy.com/study#/updates/4f241b73e4b0a2a9c2665f8a

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