Decomposição de Vetor (módulo+ângulo)

The vector decomposition calculator converts a vector given in magnitude and angle into its Cartesian components (x, y). The vector is represented as v = (|v|cosθ, |v|senθ), where θ is the angle relative to the positive x-axis. This tool is essential for transforming polar representations into rectangular coordinates, facilitating calculations in physics, engineering, and mathematics.

How it works: enter the vector magnitude and the angle (in degrees or radians). The calculator applies the cosine and sine functions to obtain the horizontal (x) and vertical (y) components. The result is displayed as an ordered pair (x, y). The angle is measured from the positive x-axis, counterclockwise.

When to use: in physics problems, such as decomposing forces, velocities, or displacements; in engineering for vector analysis on inclined planes; in navigation and computer graphics. For example, decompose a force of 100 N at 30° into horizontal and vertical components to calculate work or equilibrium.

Cautions: ensure the angle is in the correct mode (degrees or radians). Remember that angles above 360° or negative can be reduced to the [0°, 360°) range. The calculator assumes the angle is measured from the positive x-axis. For angles in radians, ensure the value is correct (e.g., π rad = 180°).