Please forgive my lack of knowledge, which i think it's one of those basic formula related to Trigonometry.
Let's look at visual example:
https://drive.google.com/file/d/0BwoMn9VKDw-tSVNRMm9RWGp3dTg/view?usp=sharing
I have 5 lines, with their line equation (let's say they have zero offset ok)
how can i calculate the Theta of each line equation make (in Pi)? (i would appreciate if you explain in detail so i understand the concept)
also I have seen this:
https://drive.google.com/file/d/0BwoMn9VKDw-tZndRMW41Qnc1aUk/view?usp=sharing
Are they generated from Theta of line equations? or it's another theory which help to find the theta?
much appreciate your time and effort
We wish to find the angle between each line (passing through the origin) and the horizontal axis, given the equations of the lines.
Notice that for a given line through the origin, the slope is $m = \frac{\Delta y}{\Delta x}.$ As such, this is identical to the definition of tangent, which states $\tan(\theta) = \frac{\text{opp}}{\text{adj}}.$ We can now write that $\tan(\theta) = m.$ Given the value of $m,$ we can find $\theta$ with the relation $\boxed{\theta = \arctan(m)}.$