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The axes are rotated through an angle pi...

The axes are rotated through an angle `pi//3` in the anticlockwise direction with respect to `(0,0)`. Find the coordinates of point `(4,2)` (w.r.t. old coordinate system) in the new coordinates system.

Text Solution

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Here, `(x,y)=-=(4,2)`
and `theta =pi//(3)`
`therefore X=xcos theta+ y sin theta`
`=4 cos (pi)/(3) +2sin(pi)/(3)`
`=4xx(1)/(2)+2xxsqrt(3)/(2)=2+sqrt(3)`
and `Y=-xsintheta+ycostheta`
`=-4sin(pi)/(3)+2cos(pi)/(3)`
`=-4xx(sqrt3)/(2)+2xx(1)/(2)=-2sqrt(3)+1`
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