Bus turning radius

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

Bus turning radius

Postby Guest » Wed Dec 06, 2017 4:36 am

Context
I have a bus, at position {x, y}. It is going in a direction d, in radians.
Image
I need to draw two arcs that shows its turning radius. Let's keep to one arc.
I need to center the arc some distance i from {x,y}. Arc start and end are not important.
Of course, the arc has a radius, but its not important.
Image
Problem
Distance i, which is really {dx,dy}, becomes "skewed" when the bus turns.
When it is as I drew it previously, dy=0, dx=i. Easy.

In the general scenario,
Image
dx and dy are unknown and to be determined.
I know there's a cos and/or sin in there, but I feel like i've tried every possible combination!
I need to
a) have the formulas for dx and dy; and
b) understand how/why it works so I can do the second left-wheel arc.





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