What are the rules for expressing angles and finding vector components?

[luxor106]

Homework Statement

So I have been doing the adding of vectors by using their components and you are suppose to use the + X axis as a reference frame so when 3 vectors are given do you always have to subtract the given theta from the quardrant total ie. 22m, 56 degrees west of south plotting this places the vector with in the 3rd quadrant so you would have to do 270-56 in order to get the degree used in the vx= v cos theta or vy= vsin theta. but I have seen other problems where the vector resides in the 3rd quadrant and the solution is achieved by using the theta stated in the problem and you do not have to subtract it from the 270. So i am confused about the rules of the is process can someone please explain

Homework Equations

vx= v cos theta
vy= v sin theta

The Attempt at a Solution

 

[bob1182006]

yes your method is right,
but they might be right too, what they did can be correct if you take south to be the positive x-axis, but usually x-axis is east because we're used to it and you don't have to thing down is increasing and where would y be? O.O

 

[Vijay Bhatnagar]

There are several methods for expressing an angle, all correct. For example : an angle 110 degrees north of east can also be expressed as 70 degrees north of west. cos110 deg = -0.34 and cos70 deg = 0.34. Thus, both ways of expressing the angle lead to same result except the sign.

You can follow the rule : If all angles in a problem are given with reference to the same direction (say with reference to north) then you can use the given angles for finding the components. Signs + or - will be automatically taken care. However, if the angles given are with reference to different direction (say one wrt north, another wrt west), then be careful. To avoid making a mistake you could convert all the given angles wrt to one reference (say north).