How can the vector derivative be calculated from this photo?

[nhrock3]

from this photo its a radius multiplied by sinus which is aproximated to its angle

and the divided by dt

but i don't know how they got the expreesion on the top of the photo

from the graph on the photo

 

[tiny-tim]

shalom nhrock3!

(btw, we say sine or sin, not sinus )

|∆r| is approximately the length of the chord, which is 2r |sin(∆θ/2)|, or approximately 2r(|∆θ|/2), = r|∆θ|

and the direction of ∆r is obviously tangential, ie along θ

so ∆r = r(∆θ) θ