Angle between a vector and a line parallel with the y-axis? (image example)

Hi, I have this red point with coordinates (x1,y1) and I would like to calculate the angles that each vector departing from the red point to the black ones form with a line parallel to the y-axis. How should I do? I'm so sorry for the drawing but that is exactly the scenario. Thanks!

Answer 1

[Ameer Hamza]

Try something like this

P = [-3, 5]; % (x1,y1)
x = [0 10]; % point of y-axis
Px = x-P;
angle = atan2(Px(1), -Px(2))

[Davide Mori]

why is there -Px(2) in the atan2 function?

[Ameer Hamza]

y-axis is negative in a downward direction, whereas we want a positive x-axis in the downward direction in our rotated coordinates.

[Davide Mori]

I was checking your solution with different values. Let's put

p = [-3 0.95]
r = [0 0]  %point on the origin of axis
pr = r - p
angle = atan2(pr(1), -pr(2))

Now, I would expect an angle which is less than 90 degrees but converting instead I obtain -107 degrees, why this?

[Ameer Hamza]

I get expected answer. atan2() return the output in radians. How did you get -107 from that. When I run the following code

p = [-3 0.95]
r = [0 0]  %point on the origin of axis
pr = r - p
angle = atan2(pr(1), -pr(2))

I get

>> angle
angle =
    1.2641
>> rad2deg(angle)
ans =
   72.4287

It might be easier to use atan2d()

p = [-3 0.95]
r = [0 0]  %point on the origin of axis
pr = r - p
angle = atan2d(pr(1), -pr(2))

Result

>> angle
angle =
   72.4287

[Davide Mori]

You are right, I don't know I got that result ahahah, thank you so much!

[Ameer Hamza]

I am glad to be of help! :)