a) $\sin(\theta)$ and $\cos(\theta)$ given $\tan(\theta) =\frac{ 5}{12}$ and $\theta$ is acute
b) $\sin(\theta)$ and $\tan(\theta)$ given $\cos(\theta) = -\frac{3}{5}$ and $\theta$ is obtuse
c) $\cos(\theta)$ and $\tan(\theta)$ given $\sin(\theta)= -\frac{7}{25}$ and $270^{\circ}<\theta<360^{\circ}$
On
From the Pythagorean identity $$ \sin^2\theta+\cos^2\theta=1 $$ you can deduce, by division $$ \tan^2\theta+1=\frac{1}{\cos^2\theta} $$ and $$ 1+\frac{1}{\tan^2\theta}=\frac{1}{\sin^2\theta} $$ So, when you know one of the three functions, you can deduce the absolute value of the other two. The information about the size of $\theta$ will determine the sign.
These ratios should look like Pythagorean triangles you know and maybe love. For a, the definition of tangent is $\frac {\text {opposite}}{\text {adjacent}}$ so draw a right triangle with that tangent. What is the hypotenuse? What are the $\sin$ and $\cos?$
For the others, you can follow the same process. You need to use the minus signs to pick the quadrant.