How do I convert cartesian coordinates into polar coordinates?

Polar coordinates are expressed in the form (r,θ), where r is the distance of the point, P, from the origin, and θ (usually expressed in radians) is the angle between the line joining the point to the origin, and the positive x-axis (moving anti-clockwise from the x-axis). r can be seen as the hypotenuse of a right-angled triangle, where the base of the triangle has a length equal to the value of the x-coordinate of P, and the height of the triangle a length equal to the value of the y-coordinate of P. Therefore r can be calculated using Pythagoras' Theorem (r=(x^2+y^2)^1/2). θ can also be calculated using this right-angled triangle, since tanθ will be equal to y/x for a point in the top right quadrant (for a point in the top-left quadrant or bottom-left quadrant this value will need to be subtracted from pi, and in the case of the bottom-left quadrant made negative since the smallest angle will be going clockwise from the x-axis, and for a point in the bottom-right quadrant this value of θ will also be also made negative).

(Diagrams would be used throughout explanation)