Wrong Answer in Textbook for Collision Velocity Calculation

[mafagafo]

Homework Statement

(Problem about a collision) (...). What then is their velocity in (a) unit-vector notation and as (b) magnitude and (c) angle.

I will not post the problem due to copyright issues and that it is absolutely pointless now.

The Attempt at a Solution

I was able to solve (a) and (b).
However, my answer for (c) differs from that of the textbook.
$$\text{a)} \;(2.67 \;\text{m/s})\hat{i}+(-3.00 \;\text{m/s})\hat{j}$$
$$\text{b)} \;4.01 \;\text{m/s}$$
$$\text{c)} \;\theta{} = \tan^{-1}\left(-\frac{3.00}{2.67}\right)=-0.845397=-48.4^{\circ{}}$$

While the book provides +48.4° as the angle.

Am I correct? You can solve (c) from (a) and (b) [my answers are identical to those of the book].

It is from Fundamentals of Physics (Extended) - 9th ed.

 

[Mangoes]

Well, without thinking too much about it, the vector given in (a) is in the fourth quadrant. The angle 48.4° is in the first quadrant. Your answer, however, is definitely in the fourth quadrant.

 

[TSny]

You are correct. The text should not have stated the answer as simply 48.4^o.
If they had stated it as 48.4^o below the positive x direction, then that would have been a good answer. But they didn't.

 

[mafagafo]

Yes, that's what I thought. I was pretty sure I was right, but as this book has presented very few mistakes already I thought I could be missing something.

Thank you guys for looking at it.