What is the correct angle for a vector with components (-3.18m)i and (4.73m)j?

[goaliejoe35]

What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise.

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c03/eq03_84.gif

My Answers:

a) (-3.18m)i + (4.73m)j
b) 5.70 m
c) -56.09 degrees

Part C was marked wrong and I don't understand why... i did tan inverse of (4.73/-3.18) to get my answer. Could someone tell me what I did wrong?

 

[alphysicist]

Hi goaliejoe35,

If you draw a set of x- and y- axes on a paper and draw the vector that you gave in part a, what quadrant is it in? What quadrant is the angle the you put as the answer to part c in?

 

[goaliejoe35]

the vector from part a is in quadrant 2 right? and the angle i gave is in quadrant 4?

 

[alphysicist]

That's right. Think about your vector:

(-3.18m)i + (4.73m)j

and then think about the vector in the opposite direction:

(3.18m)i + (-4.73m)j

Use inverse tangent on both of them:

on yours: arctan( 4.73 / -3.18 ) = arctan( -1.48742)
on the other: arctan ( -4.73 / 3.18 ) = arctan(-1.48742)

and that's the problem. Most calculators can't tell the difference between the two cases, so the answer it gives is either the true answer that you're looking for, or it's in the opposite direction from what you want (180 degrees away).

So in your case, you would need to recognize that your vector is in the second quadrant, but the calculator is giving you an angle in the fourth quadrant, so you need to add 180 degrees to the calculator answer to get the real answer.

 

[goaliejoe35]

Ok awesome! Thanks for all your help!