Find the angle between the OA ray and the positive OX semiaxis, if A (-1; 3).

Two vectors are given: vector b {x; 0} axis OX and vector a {-1; 3} vector 0А.
cos A is defined as the ratio of the dot product of these vectors to the product of the moduli of the vectors.
cos А = (a · b) / | a | · | b |, where (a · b) is the scalar product of vectors a and b, | a | · | b | the product of the moduli of these vectors.
Dot product (a b) = (-1) * (x) + 0 * 3 = -x.
Modulus | a | = root [(- 1) ^ 2 + 3 ^ 2] = √ (10),
modulus | b | = √ (x ^ 2 + 0 ^ 2) = x,
cos A = – x / [√ (10) * (x)] = – 1 / √ 10 = – 0.316.
A = 108 °, since its cosine is negative, and the angle is located in the 2nd quarter.