I have 2cos^2(x)+cos(x)=1 and I have to solve for x within a standard circle(0-2pi).

Then I have to find the general solution for the above equation and 2tan(x) +SqRt(12)=0(which I previously solved for.

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- Jun 16th 2009, 07:36 PMBlahdkmSolving for X, and General solutions?
I have 2cos^2(x)+cos(x)=1 and I have to solve for x within a standard circle(0-2pi).

Then I have to find the general solution for the above equation and 2tan(x) +SqRt(12)=0(which I previously solved for. - Jun 16th 2009, 07:44 PMVonNemo19
Simply subtract one from both sides and the factor the quadratic

$\displaystyle 2cos^2x+cosx-1=0$

$\displaystyle (2cosx-1)(cosx+1)=0$

now see that cosx=1/2 or -1

what angles do these correspond to?

$\displaystyle 2tanx=-\sqrt{12}$

$\displaystyle 2tanx=-2\sqrt{3}$

$\displaystyle tanx=-\sqrt{3}$

i only know of two angles.......

any questions?

thanx mr. fantastic - Jun 16th 2009, 08:31 PMalexmahoneQuote:

$\displaystyle 2tanx=-\sqrt{12}$

$\displaystyle 2tanx=-2\sqrt{3}$

$\displaystyle tanx=-\sqrt{3}$

i only know of two angles.......

where n is an integer. - Jun 17th 2009, 03:43 AMBlahdkm
Thank you two SO MUCH for the help! Any chance of assistance finding the general solution of 2cos^2(x) + cos(x)=1?

- Jun 17th 2009, 04:08 AMalexmahone