Which method is used to find the angle of a vector given its components?

The method for finding the angle of a vector given its components is based on the relationship between the components and trigonometric functions. The correct choice, which involves using the tangent function, is particularly relevant because when you have a vector with components x (horizontal) and y (vertical), the angle θ that the vector makes with the x-axis can be found using the arctangent of the ratio of the opposite side to the adjacent side in a right triangle formed by these components.

Using the formula θ = tan⁻¹(y/x), where y is the vertical component and x is the horizontal component, effectively allows you to determine the angle based on how far the vector extends in each direction. This is appropriate because the tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to it.

The other options misapply trigonometric functions. For instance, using cosine or sine would require knowing the angle prior, and dividing x by y does not yield an angle but rather gives a different form of ratio without the necessary trigonometric context. Therefore, the correct application of the tangent function for finding angle θ ensures that the relationship between the components is properly utilized,