When tan theta is -ve why did we assume that it's in the second quad?

[Douna2nd]

The problem says
" Two forces of magnitudes 12 and 15 Newton are applied to a point and the tangesnt of the angle between them is -3/4. Find the resultant of the two forces and the measure of its angle of inclination on the first force.
In the answer it says that the theta belongs to the second quad, and I assume this is because the tan -ve but why didn't it assume it's in the fourth quad? And why doess the -ve sign belong to the 4 on the x-axis not the 3 on the y-axis??

 

[tiny-tim]

Hi Douna2nd!

" … the tangesnt of the angle between them is -3/4"

In the answer it says that the theta belongs to the second quad, and I assume this is because the tan -ve but why didn't it assume it's in the fourth quad?

Because the convention is we always take the "principal value" for arctan, and that's between 0 and π (ie, 1st or 2nd quadrant).

And why doess the -ve sign belong to the 4 on the x-axis not the 3 on the y-axis??

Not following you.

 

[LCKurtz]

And why doess the -ve sign belong to the 4 on the x-axis not the 3 on the y-axis??

Not following you.

That's because -ve is baby-talk for "negative".

 

[HallsofIvy]

Two rays, starting at the same point, create two angles, one less than or equal to 180 degrees, the other larger than or equal to (and the two angles add to 360 degrees). The angle created is, by definition, the smaller of the two.