Question

F = (-5.7,-5.7), where all components are in newtons. If a vector's direction is measured counterclockwise from the positive x-axis, what angle (in degrees from 0-360) does F make?

Answer 1

The vector F = (-5.7, -5.7) Newtons makes an angle of 225° with the positive x-axis, as it lies in the third quadrant.

Step-by-step explanation:

To determine the angle that vector F makes with the positive x-axis, where F = (-5.7, -5.7) Newtons, we use trigonometry. Since both components are negative, the vector lies in the third quadrant. The angle with the x-axis in this quadrant ranges from 180° to 270°.

To find the specific angle, we calculate the arctan of the ratio of the y-component to the x-component. However, given that arctan returns values between -90° and 90°, we need to adjust it because we're in the third quadrant. The formula is:

Angle with the x-axis = arctan(|Fy/Fx|) + 180°

In this case:

Angle with the x-axis = arctan(|-5.7/-5.7|) + 180° = arctan(1) + 180° = 45° + 180° = 225°

Therefore, vector F makes an angle of 225° with the positive x-axis.