Answer:
[tex]\theta = 148.8[/tex]
Step-by-step explanation:
Given
[tex]R_x = -419[/tex]
[tex]R_y = -253[/tex]
[tex]R = 490[/tex]
Required
Determine the value of [tex]\theta[/tex]
Since, [tex]\theta[/tex] is counter clockwise from x axis;
The relationship between [tex]\theta[/tex], [tex]R_x[/tex] and R is
[tex]cos\theta = \frac{R_x}{R}[/tex]
Substitute values for Rx and R
[tex]cos\theta = \frac{-419}{490}[/tex]
[tex]cos\theta = -0.8551[/tex]
Take arccos of both sides
[tex]\theta = cos^{-1}(-0.8551)[/tex]
[tex]\theta = 148.770784108[/tex]
[tex]\theta = 148.8[/tex] (Approximated)
