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

| September 28, 2021 | education

Let us write the equation of a straight line of the form y = kx + b, which passes through the origin of coordinates O (0; 0) and point A (–1; 3).

Then the slope k of this straight line will be equal to the tangent of the angle between the given straight line and the positive semiaxis Ox.

If the straight line y = kx + b passes through the point O (x1; y1), then the following relation is true:
y1 = kx1 + b.

Since this line passes through the origin of coordinates О (0; 0), the following relation is true:

0 = k * 0 + b.

hence b = 0.

Since this line passes through point A (–1; 3), the following relation is true:

3 = k * (-1).

Therefore, k = -3 and the tangent of the angle between this straight line and the positive semiaxis Ox is -3.

Since this angle lies in the second quarter, the value of this angle is arctan (-3).

Since arctan x is odd, arctan (-3) = – arctan 3.

Answer: the desired angle is -arctg 3.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.