Let $\displaystyle sin \alpha =\frac{-1}{4}, \pi < \alpha < \frac{3\pi }{2}$.
Find: $\displaystyle tan(\alpha -\frac{25\pi }{4})$
draw a reference triangle in quad III, use the given $\displaystyle \sin{\alpha} = -\dfrac{1}{4}$ to determine the value of $\displaystyle \cos{\alpha}$ , then use the ratio identity to find $\displaystyle \tan{\alpha}$ , finally use the difference identity for tangent to finish.
btw ... you need to be sharing what you've attempted on all those other posts.