If the axes are rotated through an angle of 30° in clockwise direction, the point (4, 23) in the new system is

We have x=4,y=23 and θ=−30∘∴ X=xcos⁡θ+ysin⁡θ and Y=−xsin⁡θ+ycos⁡θ⇒ X=4cos⁡30∘−23sin⁡30∘Y=+4sin⁡30∘+23cos⁡30∘=X=3 and Y=5Hence, the given point in the new system is (3,5)