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mathslover Group Title

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

  • one year ago
  • one year ago

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  1. Yahoo! Group Title
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    \[Sin^2\theta = 1-\cos^2 \theta\]

    • one year ago
  2. Yahoo! Group Title
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    Nw Form a Quadratic Equation...

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

    • one year ago
  4. mathslover Group Title
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    theta = 60 degrees.

    • one year ago
  5. mathslover Group Title
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    but general solution???

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

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

    • one year ago
  8. terenzreignz Group Title
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    wait, no, k(360 degrees) not 2k sorry

    • one year ago
  9. calculusfunctions Group Title
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    May I explain?

    • one year ago
  10. mathslover Group Title
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    Yea @calculusfunctions sir, please!

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

    • one year ago
  12. mathslover Group Title
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    I had got this : cos theta = 1/2 , please explain after this.

    • one year ago
  13. Yahoo! Group Title
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    There Will be Two value For Cos x @mathslover

    • one year ago
  14. mathslover Group Title
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    Yes but the negative one will NOT BE ACCEPTED..

    • one year ago
  15. mathslover Group Title
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    as cos x can NOT BE NEGATIVE @Yahoo!

    • one year ago
  16. Yahoo! Group Title
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    Why min value of cos x = -1 ....

    • one year ago
  17. terenzreignz Group Title
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    Must x be in degrees?

    • one year ago
  18. terenzreignz Group Title
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    theta rather

    • one year ago
  19. Yahoo! Group Title
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    \[\cos 180 = -1\]

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

    • one year ago
  21. mathslover Group Title
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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)

    • one year ago
  22. mathslover Group Title
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    cos(theta) \(\ne\) -5/2

    • one year ago
  23. Yahoo! Group Title
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    Yup.....nw u r Correct

    • one year ago
  24. calculusfunctions Group Title
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    @mathslover Let me know when you're interested in learning a more efficient method.

    • one year ago
  25. mathslover Group Title
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    @calculusfunctions sir, thanks a lot , I think I got it now.

    • one year ago
  26. mathslover Group Title
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    Sorry but do you have any easier or another way?

    • one year ago
  27. calculusfunctions Group Title
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    Yes if you're interested.

    • one year ago
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