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(A) When the axes are rotated by an angle $	heta$ in the clockwise direction,the new coordinates $(x', y')$ of a point $(x, y)$ are given by the tran

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$(2 + \sqrt{3}, -2\sqrt{3} + 1)$

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(A) When the axes are rotated by an angle $	heta$ in the clockwise direction,the new coordinates $(x', y')$ of a point $(x, y)$ are given by the transformation equations:$x' = x \cos 	heta + y \sin 	heta$$y' = -x \sin 	heta + y \cos 	heta$Given $x = 4$,$y = 2$,and $	heta = \frac{\pi}{3}$,we have $\cos \frac{\pi}{3} = \frac{1}{2}$ and $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$.Substituting these values:$x' = 4 \left(\frac{1}{2}ight) + 2 \left(\frac{\sqrt{3}}{2}ight) = 2 + \sqrt{3}$$y' = -4 \left(\frac{\sqrt{3}}{2}ight) + 2 \left(\frac{1}{2}ight) = -2\sqrt{3} + 1$Thus,the new coordinates are $(2 + \sqrt{3}, -2\sqrt{3} + 1)$.

If the axes are rotated through an angle $\theta = \frac{\pi}{3}$ in the clockwise direction with respect to the origin $(0, 0)$,what are the coordinates of the point $(4, 2)$ in the new system?

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