Question

A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.

Answer 1

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Answer:

23°

Explanation:

The angle a vector makes relative to the +x axis is found as ...

α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°

The angle is about 23°.

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Additional comment

This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)