Cartesian coordinate system
Rotation

To rotate a figure counterclockwise around the origin by some angle θ {\displaystyle \theta } is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x ', y '), where

x ′ = x cos θ − y sin θ y ′ = x sin θ + y cos θ. {\displaystyle {\begin{aligned}x'&=x\cos \theta -y\sin \theta \\y'&=x\sin \theta +y\cos \theta.\end{aligned}}}

Thus:

(x ′, y ′) = ((x cos θ − y sin θ), (x sin θ + y cos θ)). {\displaystyle (x',y')=((x\cos \theta -y\sin \theta \,),(x\sin \theta +y\cos \theta \,)).}
combination:two_responses