Answer :
To determine the angle of a vector given its x-component and y-component, we can use the inverse tangent function (also known as arctan or [tex]\tan^{-1}[/tex]).
Here's how you can calculate it step by step:
Identify the components of the vector:
- The x-component of the vector is 5.
- The y-component of the vector is 4.
Use the arctan function to find the angle:
The formula to find the angle [tex]\theta[/tex] of the vector relative to the positive x-axis is:
[tex]\theta = \tan^{-1} \left( \frac{y}{x} \right)[/tex]Substitute the given values into the formula:
[tex]\theta = \tan^{-1} \left( \frac{4}{5} \right)[/tex]Calculate the angle:
Using a calculator, find [tex]\theta = \tan^{-1} \left( 0.8 \right)[/tex].The angle [tex]\theta[/tex] is approximately [tex]38.7^\circ[/tex].
This matches one of the multiple-choice options provided, which is C. 38.7. Therefore, the angle of the vector is approximately [tex]38.7^\circ[/tex].