Trigonometry
We know that

Using the third equation we are going to find cos∅:
![\begin{gathered} \sin ^2\phi+\cos ^2\phi=1 \\ \cos ^2\phi=1-\sin ^2\phi \\ \cos ^2\phi=1-(-(4)/(5))^2 \\ \cos ^2\phi=1-(16)/(25) \\ \cos ^2\phi=(9)/(25) \\ \cos \phi=\pm\sqrt[]{(9)/(25)} \\ \cos \phi=\pm(3)/(5) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/vxxye842iesp633aly9wrcf2uhewpqxhuk.png)
We, have two possibilities cos∅ is positive or cos∅ is negative.
By the first equation and the given information Tan∅ > 0, we know that

Since sin∅ is negative, and sin∅/cos∅ is positive, cos∅ must be negative so tan∅ > 0. Then

Using the second equation, we have that:

Answer: cos∅= -3/5 and cot∅ = 3/4