Can you guys help with verifying my work for this problem. My answers don't match the given answers.
Given $\tan 2\theta = -\dfrac{-24}{7}$, where $\theta$ is an acute angle, find $\sin \theta$ and $\cos \theta$
I used the identity, $\tan 2\theta = \dfrac{2\tan \theta}{1 - tan^2 \theta}$ to try and get an equation in $\tan \theta$.
$ \begin{align} -\dfrac{24}{7} &= \dfrac{2\tan \theta}{1 - \tan^2 \theta} \\ -24 + 24\tan^2 \theta &= 14 \tan \theta \\ 24tan^2 \theta - 14\tan \theta - 24 &= 0 \\ 12tan^2 \theta - 7\tan \theta - 12 &= 0 \\ \end{align} $
Solving this quadratic I got, $ \tan \theta = \dfrac{3}{2} \text{ or } \tan \theta = -\dfrac{3}{4}$
$\therefore \sin \theta = \pm \dfrac{3}{\sqrt{13}} \text{ and } \cos \theta = \pm \dfrac{2}{\sqrt{13}}$
Or,
$\therefore \sin \theta = \pm \dfrac{3}{5} \text{ and } \cos \theta = \mp \dfrac{4}{5}$
The given answer is,
$\sin \theta = \dfrac{4}{5} \text{ and } \cos \theta = \dfrac{3}{5}$
I thought I needed to discard the negative solution assuming $\theta$ is acute. But they haven't indicated a quadrant. Do I assume the quadrant is I only? What am i missing? Thanks again for your help.