I was working through this question: find the 5 missing ratios in $\tan \theta=\frac{7\sqrt{2}}{8}, and \cos<0.$  

I thought I had found a shortcut where I could use trig identities in order to find $\sin\theta$ and $\cos\theta$ given the identity $\tan\theta = \frac{\sin\theta}{\cos\theta}$, meaning that $\sin\theta=7\sqrt{2}$ and $\cos\theta = 8$. Obviously, this is not the case given that the range of $\sin\theta = [-1,1]$. Why is this the case? Where did my thinking fall apart?