Suppose that a material point instead of move itself along a circle in clockwise direction as shown in the figure moves, instead, in counterclockwise direction.
$$ \vec{v}_1=(v \cos(π−ϕ)){\bf \hat x}+(v \sin(π−ϕ)) {\bf \hat y} $$ and $$\vec{v}_2=(v \cos(π+ϕ)){\bf \hat x}+(v \sin(π+ϕ)) {\bf \hat y}$$
I must to find the quantity $-2(v \sin(ϕ)) {\bf \hat y}$. In fact
$$\overrightarrow{\Delta v}=\vec{v}_2 - \vec{v}_1 = (-v \cos(ϕ)){\bf \hat x}-(v \sin(ϕ)) {\bf \hat y} + v \cos(ϕ) {\bf \hat x} -(v \sin(ϕ)) {\bf \hat y}=-2(v \sin(ϕ)) {\bf \hat y}$$
Please, are they correct my steps?