Answer
$$\cos x=-\frac{4}{5}$$
$$\tan x=-\frac{3}{4}$$
Work Step by Step
$$\sin x = \frac{3}{5}, x\in\Big[\frac{\pi}{2},\pi\Big]$$
1) As $x\in\Big[\frac{\pi}{2},\pi\Big]$, it means angle $x$ is in the second quadrant, so $\cos x\lt0$ and $\tan x\lt0$.
2) To find $\cos x$, we employ the formula: $$\cos^2 x+\sin^2x=1$$
$$\cos^2x=1-\sin^2x=1-\Big(\frac{3}{5}\Big)^2=1-\frac{9}{25}=\frac{16}{25}$$
$$|\cos x|=\frac{4}{5}$$
Since $\cos x\lt0$, $$\cos x=-\frac{4}{5}$$
3) To find $\tan x$, we employ the formula:
$$\tan x=\frac{\sin x}{\cos x}=\frac{\frac{3}{5}}{-\frac{4}{5}}=-\frac{3}{4}$$
