Question

The diagram shows components that have been added together to form Rx and Ry. Rx and Ry are the components of the resultant vector.

Three vectors drawn on the x y plane. The first vector is drawn in the positive x direction along the x axis and labeled R Subscript x Baseline. The second is drawn tail to tip method north and labeled R Subscript y Baseline. The last is drawn from the tail of the first to the head of the second and labeled R. The angle between R and R Subscript x Baseline is labeled theta.



Which formula can be used to find the angle of the resultant vector?

Answer 1

To find the angle (
`\( \theta \)`) between the resultant vector (
`\( \mathbf{R} \)`) and its x-axis component (
`\( \mathbf{R}_x \)`), use the formula
`\( \theta = \arctan\left((R_y)/(R_x)\right) \)`. This formula involves the arctangent function and considers the vector components along the x and y axes.

To find the angle (
`\( \theta \)`) between the resultant vector (
`\( \mathbf{R} \)`) and the x-axis component (
`\( \mathbf{R}_x \)`), you can use the arctangent (inverse tangent) function. The formula is:

`\[ \theta = \arctan\left((R_y)/(R_x)\right) \]`

Here:

-
`\( R_y \)` is the y-axis component of the resultant vector (
`\( \mathbf{R}_y \)`),

-
`\( R_x \)` is the x-axis component of the resultant vector (
`\( \mathbf{R}_x \)`).

This formula is based on the definition of tangent in a right-angled triangle. The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case,
`\( R_y \)` is opposite to the angle
`\( \theta \)`, and
`\( R_x \)` is adjacent to
`\( \theta \)`. The arctangent function gives you the angle whose tangent is the specified ratio.