What is the direction angle of vector <-2,-5>?

[(-_-)]

Homework Statement

Find the direction angle of vector <-2,-5>

Homework Equations

The components of a vector is v=<magnitude*cos ø, magnitude*sin ø>
Magnitude of a vector: √(a^2+b^2)

The Attempt at a Solution

I found the magnitude of the vector, which is √29. Then I set -2= √29 cos ø and solved for ø. It was 111.891 degrees but the answer to the problem was 360 MINUS 111.891 degrees. I thought it would be 180 PLUS 111.891.

 

[abhikesbhat]

Ok you could draw the point in the plane. Make a right triangle with legs 2,5. You could then arcTan of that. That angle is the angle it makes with negative x-axis and negative y-axis. Since you are measuring from the positive x you add 180 to that. That is the angle.

 

[jacksonpeeble]

360-111.891 is logical because of where on the coordinate plane you measure from.

By the way, welcome to the forums!

 

[robphy]

http://www28.wolframalpha.com/input/?i=degrees+(Arctan(-5/-2))
http://www28.wolframalpha.com/input/?i=degrees+(Arctan(-5/-2)+Pi)
Use arctan(y/x)... if x<0, add 180 to what the calculator function arctan gives you.
You can deduce this rule by studying various cases and graphing.
(You might try to deduce similar rules for arccos and arcsin.)

http://www28.wolframalpha.com/input/?i=Arctan(-2,-5)