Let θ be the angle that the vector A ⃗ makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components:

Question Source- Young, H. D., Freedman, R. A., & Ford, A. L. (2020). University Physics with Modern Physics (Most Editions). Pearson. Online Purchase [https://amzn.to/4f6yCuY]

[1.8] Components of Vectors.

First identify the appropriate formula for finding an angle between vectors.

tanθ=A_y/A_x

[a] A_x=2.00 m, A_y=-1.00 m,

1st note that the vector resides in quadrant IV

arctan[(-1.00)/2.00]=-26.57° ⇒ θ=360°-26.57°=333.43°

[b] A_x=2.00 m, A_y=1.00 m,

θ=arctan[1.00/2.00]=26.57°

[c] A_x=-2.00 m, A_y=1.00 m,

Resides in QII

arctan[1.00/(-2.00)]=-26.57° ⇒ θ=180°-26.57°=153.43°

[d] A_x=-2.00 m, A_y=-1.00 m.

In Q III

Since both are negative, we know from [b] that the result is 26.57° and we add 180° to it

θ=206.57°.

There is no reference to sig figs. Do what you feel is appropriate or asked for.