mathslover
find the general solution for : \(\sin^2 \theta -2 \cos \theta + \frac{1}{4} = 0 \)
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Yahoo!
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\[Sin^2\theta = 1-\cos^2 \theta\]
Yahoo!
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Nw Form a Quadratic Equation...
mathslover
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I got \(\theta = \cos^{-1} \frac{1}{2}\)
mathslover
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theta = 60 degrees.
mathslover
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but general solution???
terenzreignz
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Just add 2k(360 degrees) where k is any integer, and there's your general solution :D
Yahoo!
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\[\cos \theta =\frac{ 1 }{ 2 }\]
\[Cosx=Cosy\]
then
\[x=(2n \Pi)\pm y\]
terenzreignz
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wait, no, k(360 degrees) not 2k sorry
calculusfunctions
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May I explain?
mathslover
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Yea @calculusfunctions sir, please!
Yahoo!
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\[x= (2n \Pi) \pm \frac{ \Pi }{ 3 }\]
mathslover
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I had got this : cos theta = 1/2 , please explain after this.
Yahoo!
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There Will be Two value For Cos x @mathslover
mathslover
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Yes but the negative one will NOT BE ACCEPTED..
mathslover
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as cos x can NOT BE NEGATIVE @Yahoo!
Yahoo!
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Why min value of cos x = -1 ....
terenzreignz
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Must x be in degrees?
terenzreignz
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theta rather
Yahoo!
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\[\cos 180 = -1\]
calculusfunctions
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\[\sin ^{2}\theta -2\cos \theta +\frac{ 1 }{ 4 }=0\]First multiply the equation by the least common denominator.
mathslover
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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)
mathslover
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cos(theta) \(\ne\) -5/2
Yahoo!
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Yup.....nw u r Correct
calculusfunctions
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@mathslover Let me know when you're interested in learning a more efficient method.
mathslover
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@calculusfunctions sir, thanks a lot , I think I got it now.
mathslover
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Sorry but do you have any easier or another way?
calculusfunctions
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Yes if you're interested.