Definition of polar angle and its code implementation

Definition of polar angle

As shown in the figure , In polar coordinates , Every point M, Can use its distance from the origin O Distance of $\rho$ and OM And x Angle between axes $\theta$ Sole determination .M The polar coordinates of are $(\rho ,\theta )$, among $\theta$ Is the polar angle .

Calculation of polar angle

set up M The coordinates of the point in the rectangular coordinate system are $(x,y)$, origin O The coordinates of the for $(0,0)$, Then there is the following equation relation with polar coordinates ：
$\{\begin{array}{l}\rho =x^2+y^2\\ \tan (\theta )=\frac{y}{x}(x\ne 0)\end{array}$ or $\{\begin{array}{l}x=\rho \cos (\theta )\\ y=\rho \sin (\theta )\end{array}$
therefore , Polar angle $\theta =\arctan (\frac{y}{x})$

Code implementation

Use java.lang.Math Of atan2 function , For point M$(x,y)$, It is the same as the origin O$(0,0)$ Polar angle of $\theta =Math.atan2(y,x)$

public static double atan2(double y, double x)

If O The coordinates of the for $(x_0,y_0)$, spot M$(x,y)$ And O The polar angle of is $\theta =Math.atan2(y-y_0,x-x_0)$