What is the formula for calculating the angle (theta) of a vector?

The correct formula for calculating the angle (theta) of a vector in a two-dimensional Cartesian coordinate system is given by theta = tan^(-1)(y / x). This formula is derived from the definition of the tangent function, which relates the opposite side of a right triangle to the adjacent side.

In this context, y represents the vertical component of the vector, and x represents the horizontal component. The angle theta can be calculated by taking the arctangent (or inverse tangent) of the ratio of the vertical and horizontal components. This is essential in determining the direction of the vector in relation to the positive x-axis.

Using the arctangent helps identify the angle between the vector and the x-axis accurately, with the angle typically falling within the range of (-90° to 90°) for direct calculations. Adjustments may be needed based on the signs of x and y to place theta in the correct quadrant.

The other formulas provided do not accurately represent the calculation for the angle of a vector in this context.