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snivvles.com

  • one year ago

Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5

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  1. Nnesha
    • one year ago
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    let sinx = y \[\huge\rm 7y^2-14y+2=-5\] now you have quadratic equation set it equal to zero (move -5 to the left side)

  2. snivvles.com
    • one year ago
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    so \[7y ^{2}-14y+7=0\]?

  3. Nnesha
    • one year ago
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    yes right now can you solve for y ?

  4. snivvles.com
    • one year ago
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    \[\frac{ 14+-\sqrt{196-4(7)(7)} }{ 2(7) }\]

  5. Nnesha
    • one year ago
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    oh wait you can take out the common factor

  6. Nnesha
    • one year ago
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    \[\huge\rm 7y ^{2}-14y+7=0\] what is gcf ?

  7. snivvles.com
    • one year ago
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    7 so \[\frac{ 2+-\sqrt{4-4} }{ 2 }\]

  8. Nnesha
    • one year ago
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    right!

  9. snivvles.com
    • one year ago
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    so \[\frac{ 2 }{ 2 }\]

  10. snivvles.com
    • one year ago
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    then I find where that happens on the unit circle, right?

  11. snivvles.com
    • one year ago
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    but it simplifies to \[\frac{ 1 }{ 1 }\]

  12. Nnesha
    • one year ago
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    yes right so \[\large\rm \frac{ 2 +0 }{ 2} ~and~ \frac{ 2-0 }{ 2 }\] both equal to one y= 1 now you can replace y with sinx sin x =1 sin x =1

  13. snivvles.com
    • one year ago
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    so \[\frac{ \pi }{ 2 }\]

  14. snivvles.com
    • one year ago
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    right?

  15. Nnesha
    • one year ago
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    find `all solution`

  16. Nnesha
    • one year ago
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    wait do you need in radians or degree ?

  17. snivvles.com
    • one year ago
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    so 3pi/2 5pi/2 7pi/2 etc. ?

  18. snivvles.com
    • one year ago
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    radians

  19. Nnesha
    • one year ago
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    yes pi /2 is right !

  20. snivvles.com
    • one year ago
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    is 3pi/2 right?

  21. Nnesha
    • one year ago
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    sinx = positive one

  22. snivvles.com
    • one year ago
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    oh right so is 5pi/2 right?

  23. snivvles.com
    • one year ago
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    so like pi/2 5pi/2 9pi/2 etc.

  24. snivvles.com
    • one year ago
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    right?

  25. Nnesha
    • one year ago
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    yes 5pi/2 can be the solutions

  26. snivvles.com
    • one year ago
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    Ok, thanks!

  27. Nnesha
    • one year ago
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    but remember sinx =1 (multiplicity of 2)(sinx= 1 , sinx =1)

  28. Nnesha
    • one year ago
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    np good job!

  29. snivvles.com
    • one year ago
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    OK!

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