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Sin x = 4/5          or     - 3/5

Cos x = -3/5        or     4/5                 

for quadrant II     sin is positive    so   4/5   

                          and cos is negative    so   -3/5

then tan = sin/cos =  4/5 / -3/5 =  - 4/3

Thanks for answering EP 

But I do not understand your logic.

Here's a little more detail: