Why should I consider size of revolving line always to be positive in unit circle, trigonometry?

Question

I'm reading a book, Plane Trigonometry by SL Loney.

Consider the diagram in article 50. In according to Article 50 OB' and OA' is negative direction and OB and OA are positive. In Aricle 52(First Quadrant:) OP₁ is considered positive. In (Second Quadrant:) M₂O is considered negative while P₂ is considered positive. This is why sine of angle is considered to be positive in 2^nd quadrant.

My question is if OP₂ is running towards negative side why don we considered its length to be negative?