The components of Vector A are given as follows

[Mdhiggenz]

Homework Statement

The components of Vector A are given as follows

A_x=+3.9

A_y=-4

The angle measured counterclockwise from the x-axis to vector A , in degrees, is closest to:

Homework Equations

arctan(y/x)= theta

The Attempt at a Solution

Hey guys, I got the answer doing Arctan (-4/3.9) +360

My question is how do we know to add 360? Do we always add 360 when it is counterclockwise to the x-axis? and what about if they asked if it was clockwise to the x-axis or vica versa for the Y axis, would we have to treat it any different.

Thank you

 

[Delphi51]

Personally, I would make a sketch to see what quadrant the vector is in. Then add 90, 180 or 270 degrees to whatever the calculator said in order to get the angle in the correct quadrant.

 

[Mdhiggenz]

Would it have anything to do since Tan is positive in quadrant four they add 360 to get an answer in quadrant four?

 

[LearninDaMath]

The xy coordinates/components gave you a line in the 4th quadrant. In a calculator, arctan will always produce an angle between ∏/2 and -∏/2. Thus, the arctan in a calculator can not produce an angle greater than 90 degrees, so if your line is in the 4 quadrant, arctan in a calculator will provide the angle between 90 and -90. And that happens to be a negative angle. If you want the positive version of that angle, you will have to go around like a clock one full turn to get the other angle that matches the position of your line.

If that didn't make sense, I am sorry and don't worry, someone will come by and provide a clearer explanation.