Let us consider equation:
$u=-q\cos(wx)$ where $q$ and $w$ are constants.
I'm looking for values of $x$ where $u$ is positive so I write
So when I solve the sign changes (right?), because of the $-q$, and I get
Then I take the inverse and end up with
$wx < \pi/2$ as a possible answer (right?),
so then $x < (\pi/2)(1/w),$
then if I assign $x_1=d(\pi/2)(1/x)$, where $0<d<1$, then $x_1$ can be an answer (right?) because $x_1$ will always be less than $(\pi/2)(1/w)$ as required by the inequality.
However, when I plug in $x_1$ into the original $u=-q\cos(wx)$ I end up with
$u=-q\cos(d(\pi/2))$ with $0<d<1,$
but this isn't correct because cosine is positive for angles less than $\pi/2$ but greater than 0, which is what I end up with in the argument, $d(\pi/2)$, and multiplying it by the negative $q$ will result in a negative $u$, which is not what I'm looking for because I'm looking for positive $u$'s.
So there it is, I think im solving the inequality wrong and that's why I'm getting the wrong answer. Please help, I can't solve this inequality.