Answer
$\theta = \tan ^{-1} \frac {3}{4} \approx 36.8 ^{\circ} $
Work Step by Step
The given vector has x-component 8 and y-component 6. Thus, this vector can be drawn as an arrow going from the origin to the point (8, 6). The vector can then be considered the hypotenuse of a right triangle with horizontal leg 8 and vertical leg 6. If we let $\theta $ be the angle between the positive direction of the x-axis and the vector, we can then write:
$\tan \theta = \frac {6}{8} = \frac {3}{4} $
To get $\theta$, we use the inverse tangent function:
$\theta = \tan ^{-1} \frac {3}{4} \approx 36.8 ^{\circ} $
This answer is correct because the vector is in the first quadrant and so $0 ^{\circ} \lt \theta \lt 90 ^{\circ}$.
