# Thread: General Solutions to Equations...

1. ## General Solutions to Equations...

How can I find the general solutions to the following equations where 0 < x < 2pi?

2cos^2x + cosx = 1

2tanx + square root of 12 = 0

Thanks.

2. Originally Posted by oryxncrake
How can I find the general solutions to the following equations where 0 < x < 2pi?

2cos^2x + cosx = 1

$\textcolor{red}{2\cos^2(x) + \cos(x) - 1 = 0}
$

$\textcolor{red}{[2\cos(x) - 1][\cos(x) + 1] = 0}$

set each factor = 0 and solve for cosx ... solutions for x will be unit circle values

2tanx + square root of 12 = 0

$\textcolor{red}{2\tan(x) + 2\sqrt{3} = 0}$

$\textcolor{red}{\tan(x) = -\sqrt{3}}$

look for solutions on your unit circle
...