If the axes are rotated by an angle of -pi /3 | vedclass

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Question

(C) Let the original coordinates be $(x, y)$ and the new coordinates be $(x', y') = (4, 2)$. The angle of rotation is $	heta = -\pi / 3 = -60^{\circ}

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the original coordinates be $(x, y)$ and the new coordinates be $(x', y') = (4, 2)$. The angle of rotation is $	heta = -\pi / 3 = -60^{\circ}$.The transformation equations for rotation of axes are:$x = x' \cos 	heta - y' \sin 	heta$$y = x' \sin 	heta + y' \cos 	heta$Substituting the values:$x = 4 \cos(-60^{\circ}) - 2 \sin(-60^{\circ})$$x = 4(1/2) - 2(-\sqrt{3}/2) = 2 + \sqrt{3}$$y = 4 \sin(-60^{\circ}) + 2 \cos(-60^{\circ})$$y = 4(-\sqrt{3}/2) + 2(1/2) = -2\sqrt{3} + 1$Thus,the original coordinates are $(2 + \sqrt{3}, -2\sqrt{3} + 1)$.

If the axes are rotated by an angle of $-\pi /3$ in the negative direction and the coordinates of a point in the new system are $(4, 2)$,find the coordinates of the point in the original system.

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