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:
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:
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
1 Answer
$\begingroup$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 $\boxed{\theta = \arctan(m)}.$
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