Question

If the axes are rotated through an angle of `30^@` in the anti clockwise direction, then coordinates of point `(4,-2sqrt3)` with respect to new axes are
A. (2,3)
B. `(2,sqrt(3))`
C. `(sqrt(3),2)`
D. `(sqrt(3),5)`

Answer 1

Correct Answer - D
We have `x=4,y= 2sqrt(3) and theta=-30^(@)`
`:. X cos theta+y sin theta and Y =-x sin theta + y cos theta`
`rArr X=4 cos 30^(@)-2sqrt(3) sin 30^(@)`
`and Y=4 cos 30^(@)+2 sqrt(3) cos 30^(@)`
`rArr X=sqrt(3) and Y=5`
Hence, the given point in the new systeme is `(sqrt(3),5)`