The point $\left(-2\,3\right)$ is in the second quadrant of the Cartesian plane where $\arctan \left(y\,x\right)$ and $\arctan \left(y\/x\right)$ do  not agree. Hence, the formulas on the right in Table 7.1.1, modified to use the two-argument arctangent function are applied directly in Maple.

Note that the naive calculation $\mathrm{\θ}\=\arctan \left(3\/\left(-2\right)\right)$ gives $\mathrm{\θ}\doteq -0.98$, an angle in the fourth quadrant. Changing coordinates should not change the location of the point in the Cartesian plane. Hence, it is essential to use the two-argument arctangent function in this calculation.