Question

describe why the tangent ratio is positive only in quadrants 1 and 3

Answer 1

"I don't want to think about that right now. It's like complicated" - my sister

Answer 2

Between 0° and 90° [1st quadrant] tan Ф  is always increasing, then positive:
tan (0°) = 0
tan (30°) = √(3)/3 = 0.577
tan(45°) = 1
tan (60°) = √3 = 1.732
tan (89°) = 57.28

We also know that tan (Ф) = tan (180° +Ф) [ 3rd quadrant]
The same logic as above applies