Solving Vector 1: Is arctan the Only Way?

[brycenrg]

Homework Statement

V1 = -6i + 8j

Homework Equations

arctan theta

The Attempt at a Solution

arctan 8/(-6) = -53 deg

To me this is a little confusing because its negative 53 degrees which is in the fourth quadrant but i reality its in the second quadrant.
Do I always have to do an additional math plus graphical test to see where it is and the actual degree of vector 1?
For example To see the degree of V1 i have to do 180 - 53 to get an angle of 127 degrees.
But is there a way that I just plug it in and it gives me the correct degree in the right quadrant right away?

 

[SteamKing]

Homework Statement

V1 = -6i + 8j

Homework Equations

arctan theta

The Attempt at a Solution

arctan 8/(-6) = -53 deg

To me this is a little confusing because its negative 53 degrees which is in the fourth quadrant but i reality its in the second quadrant.
Do I always have to do an additional math plus graphical test to see where it is and the actual degree of vector 1?
For example To see the degree of V1 i have to do 180 - 53 to get an angle of 127 degrees.
But is there a way that I just plug it in and it gives me the correct degree in the right quadrant right away?

Plug it in what? Your calculator?

Most calculators only determine the principal angle for the inverse tangent function, which is the angle such that -π/2 ≤ θ ≤ π/2.

Some computer languages have a built in function called ATAN2, which takes 2 arguments. This function can calculate the proper quadrant in which the angle falls.

Still, since you are furnished the components of this vector, you should be able to tell by inspection in which quadrant the angle falls. It's not that difficult.