However, when x < 0, the angle given by arctan ⁡ ( y x ) {\displaystyle \arctan({\tfrac {y}{x}})} points in the direction opposite to the correct angle, and a value of ±π (or ±180°) must be added to θ to place the point in the correct quadrant of the Euclidean plane.[1] This requires knowledge of the signs of x and y separately, which is lost when y is divided by x, hence the need for the two-variable arctangent.