Answer:
The direction angle for the vector measured clockwise from the positive x-axis is approximately 105.001°.
Step-by-step explanation:
Let be [tex]P(x,y)[/tex] a point containing the components of a vector, the direction angle for the vector regarding origin ([tex]\theta[/tex]), in sexagesimal degrees, is determined by the following formula:
[tex]\theta = \tan^{-1} \frac{y}{x}[/tex] (1)
Where:
[tex]x[/tex] - x-coordinate of the point P.
[tex]y[/tex] - y-coordinate of the point P.
Let consider that [tex]P(x,y) = (-7.765, 28.978)[/tex]. After a quick inspection, we note that vector stands in the 2nd Quadrant ([tex]x < 0 , y > 0[/tex]). Then, the direction of the angle with respect to the positive x semiaxis is:
[tex]\theta = \tan ^{-1} \left(\frac{28.978}{-7.765} \right)[/tex]
[tex]\theta \approx 105.001^{\circ}[/tex]
The direction angle for the vector measured clockwise from the positive x-axis is approximately 105.001°.
