how do you know for sure what quadrant?

[mathzeroh]

hello all! how do you know for sure which quadrant "they" want you to have your measure in?

for example:

Write each equation in normal form. Then find p, the measure of its normal, and "phi" the angle the normal makes with the positive x-axis.

21.-10x+5=-5y
i've got all the other stuff, it's just that when it comes to the angle measure of "phi," i get sonfused. I don't know how to recognize in which quadrant it should be. for this, I thought that it was this measure:
-26.57..........but the correct answer was 333 degrees, approximately.

i know that they got this by adding 360 to -26 degrees, but WHY I don't know. :confused:

thanks in advance for any help

[Janitor]

For the original line, the rise over run is 2/1. I'm sure you got that far.

The angle that such a line makes to the horizontal axis is arctan(2).

The angle the normal to that line makes to the horizontal axis is arctan(2) - 90, and it is pointing into quadrant IV, so it can be thought of as a negative angle. That gives you -26.56 degrees, or so says my calculator.

Looking at it as an angle swung counterclockwise (the positive direction of rotation in the plane, by convention) from a ray going horizontally to the right, the angle is 360 - 26.56 = 333.43.