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mathslover

  • 3 years ago

find the general solution for : \(\sin^2 \theta -2 \cos \theta + \frac{1}{4} = 0 \)

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  1. Yahoo!
    • 3 years ago
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    \[Sin^2\theta = 1-\cos^2 \theta\]

  2. Yahoo!
    • 3 years ago
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    Nw Form a Quadratic Equation...

  3. mathslover
    • 3 years ago
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    I got \(\theta = \cos^{-1} \frac{1}{2}\)

  4. mathslover
    • 3 years ago
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    theta = 60 degrees.

  5. mathslover
    • 3 years ago
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    but general solution???

  6. terenzreignz
    • 3 years ago
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    Just add 2k(360 degrees) where k is any integer, and there's your general solution :D

  7. Yahoo!
    • 3 years ago
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    \[\cos \theta =\frac{ 1 }{ 2 }\] \[Cosx=Cosy\] then \[x=(2n \Pi)\pm y\]

  8. terenzreignz
    • 3 years ago
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    wait, no, k(360 degrees) not 2k sorry

  9. calculusfunctions
    • 3 years ago
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    May I explain?

  10. mathslover
    • 3 years ago
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    Yea @calculusfunctions sir, please!

  11. Yahoo!
    • 3 years ago
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    \[x= (2n \Pi) \pm \frac{ \Pi }{ 3 }\]

  12. mathslover
    • 3 years ago
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    I had got this : cos theta = 1/2 , please explain after this.

  13. Yahoo!
    • 3 years ago
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    There Will be Two value For Cos x @mathslover

  14. mathslover
    • 3 years ago
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    Yes but the negative one will NOT BE ACCEPTED..

  15. mathslover
    • 3 years ago
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    as cos x can NOT BE NEGATIVE @Yahoo!

  16. Yahoo!
    • 3 years ago
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    Why min value of cos x = -1 ....

  17. terenzreignz
    • 3 years ago
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    Must x be in degrees?

  18. terenzreignz
    • 3 years ago
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    theta rather

  19. Yahoo!
    • 3 years ago
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    \[\cos 180 = -1\]

  20. calculusfunctions
    • 3 years ago
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    \[\sin ^{2}\theta -2\cos \theta +\frac{ 1 }{ 4 }=0\]First multiply the equation by the least common denominator.

  21. mathslover
    • 3 years ago
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    Wait, there will be two values for cos theta , the other one is -5/2 but -5/2 , but since the minimum value of cos theta is -1 and hence it can not be -5/2 is this what we must think abt @Yahoo! ? (sorry for my above explanation as : cos theta can never be negative as I thought that we are talking about cos(-theta) = cos theta)

  22. mathslover
    • 3 years ago
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    cos(theta) \(\ne\) -5/2

  23. Yahoo!
    • 3 years ago
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    Yup.....nw u r Correct

  24. calculusfunctions
    • 3 years ago
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    @mathslover Let me know when you're interested in learning a more efficient method.

  25. mathslover
    • 3 years ago
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    @calculusfunctions sir, thanks a lot , I think I got it now.

  26. mathslover
    • 3 years ago
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    Sorry but do you have any easier or another way?

  27. calculusfunctions
    • 3 years ago
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    Yes if you're interested.

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