Answer
$\cos{x}=-\dfrac{4}{5}$
$\tan{x}= -\dfrac{3}{4}$
Work Step by Step
Since $x$ lies in the second quadrant, $\cos{x}$ is negative.
Using the identity:
$$\cos{x}=-\sqrt{1-\sin^2{x}}$$
$$\cos{x}=-\sqrt{1-\left(\dfrac{3}{5}\right)^2}$$
$$\cos{x}=-\dfrac{4}{5}$$
$\because \tan{x}=\dfrac{\sin{x}}{\cos{x}}$
$\therefore \tan{x}=\dfrac{\dfrac{3}{5}}{-\dfrac{4}{5}}= -\dfrac{3}{4}$
