Solve for vectors needed to cancel out given sets of forces

[aron silvester]

Homework Statement

For this assignment, I am given sets of forces and asked to solve for the force(s) needed to cancel them out. For this case, I am asked to solve for the last vector, which is vector D. I've successfully found its x and y component, magnitude, and mass (kg). I've also checked if all of their combined x and y components added up to zero by adding the x and y components for all vectors A, B, C, and D. What I don't understand is the answer I got for the direction of vector D. When I drew a diagram for vector D, it's located in quadrant 4, since x-component is 1.23 N, and y-component is -0.37 N. The direction I got was 253 degrees, clearly, it means that the vectors should be in quadrant 3, but according to my x and y component, it's pointing in quadrant 4. Did I make a mistake when calculating the direction of vector D?

Homework Equations

It's all in my work down below in part 3.

The Attempt at a Solution

 

[magoo]

Your math looks good to me as far as the components go. I would double check your angle however. From the two components, it should be a small negative angle that is close to 360 degrees rather than 270 degrees. Definitely in the fourth quadrant.

 

[aron silvester]

Your math looks good to me as far as the components go. I would double check your angle however. From the two components, it should be a small negative angle that is close to 360 degrees rather than 270 degrees. Definitely in the fourth quadrant.

Isn't that how to find the angle by using the inverse of tangent, and we add 270 degrees because it's in the 4th quadrant?

 

[magoo]

The inverse tangent will give you the angle of -16.8 degrees. Because it's in the fourth quadrant, you need to subtract it from 360 degrees. I'm not sure where you got the equation that adds it to 270 degrees.