The $\sin \theta=\frac{3}{5}$ and $\cos \theta< 0$. Find $\tan \theta$.

Step 1 ：We are given that \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\).

Step 2 ：Since \(\sin \theta = \frac{3}{5}\), this means the ratio of the opposite side to the hypotenuse is \(\frac{3}{5}\).

Step 3 ：We also know that \(\cos \theta < 0\), which means the adjacent side is negative because cosine is the ratio of the adjacent side to the hypotenuse.

Step 4 ：We can use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find the value of \(\cos \theta\).

Step 5 ：Then, we can find the value of \(\tan \theta\) by dividing \(\sin \theta\) by \(\cos \theta\).

Step 6 ：By calculation, we find that \(\cos \theta = -0.8\) and \(\tan \theta = -0.75\).

Step 7 ：So, the final answer is \(\boxed{-0.75}\).