Vetor Polar

The Polar Vector calculator converts Cartesian coordinates (x, y) to polar coordinates (r, θ). The magnitude r is the distance from the origin to the point, computed as the square root of the sum of squares of x and y. The angle θ is obtained using the arctangent function (atan2), which considers the signs of x and y to determine the correct quadrant, resulting in angles between -π and π radians.

This tool is useful in various fields such as physics, engineering, and computer graphics, where representing vectors in polar coordinates simplifies problems involving rotations or distances. For example, when analyzing forces on a plane, the polar form facilitates calculating the resultant or direction. It is also used in navigation and robotics to determine relative positions.

When using the calculator, enter the values of x and y (real numbers). The result will display r (always non-negative) and θ in radians. Be careful with the interpretation of the angle: it is measured from the positive x-axis, counterclockwise. Remember that points on the y-axis (x=0) result in θ = π/2 or -π/2, depending on the sign of y. The calculator handles all quadrants correctly.