## Thomas' Calculus 13th Edition

$sin(x)=-\frac{2\sqrt 2}{3}$ and $tan(x)=-2\sqrt 2$
Given $cos(x)=\frac{1}{3}$ and $x\in[-\frac{\pi}{2},0]$, we can predict that both $sin(x)$ and $tan(x)$ will be negative. The three sides of the right triangle can be chosen as $1,2\sqrt 2, 3$, so $sin(x)=-\frac{2\sqrt 2}{3}$ and $tan(x)=-2\sqrt 2$