Question

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

Answer 1

\[Sin^2\theta = 1-\cos^2 \theta\]

Answer 2

Nw Form a Quadratic Equation...

Answer 3

I got \(\theta = \cos^{-1} \frac{1}{2}\)

Answer 4

theta = 60 degrees.

Answer 5

but general solution???

Answer 6

Just add 2k(360 degrees) where k is any integer, and there's your general solution :D

Answer 7

\[\cos \theta =\frac{ 1 }{ 2 }\]

\[Cosx=Cosy\]

then

\[x=(2n \Pi)\pm y\]

Answer 8

wait, no, k(360 degrees) not 2k sorry

Answer 9

May I explain?

Answer 10

Yea @calculusfunctions sir, please!

Answer 11

\[x= (2n \Pi) \pm \frac{ \Pi }{ 3 }\]

Answer 12

I had got this : cos theta = 1/2 , please explain after this.

Answer 13

There Will be Two value For Cos x @mathslover

Answer 14

Yes but the negative one will NOT BE ACCEPTED..

Answer 15

as cos x can NOT BE NEGATIVE @Yahoo!

Answer 16

Why min value of cos x = -1 ....

Answer 17

Must x be in degrees?

Answer 18

theta rather

Answer 19

\[\cos 180 = -1\]

Answer 20

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

Answer 21

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)

Answer 22

cos(theta) \(\ne\) -5/2

Answer 23

Yup.....nw u r Correct

Answer 24

@mathslover Let me know when you're interested in learning a more efficient method.

Answer 25

@calculusfunctions sir, thanks a lot , I think I got it now.

Answer 26

Sorry but do you have any easier or another way?

Answer 27

Yes if you're interested.