UPSEE Solved Model Paper 4

We have, x = 4, y = 2√3 and θ = - 30°
∴ X = x cos θ + y sin θ
and Y = - x sin θ + y cos θ
⇒ X = 4 cos 30° - 2√3 sin 30°
= 4 ×

√3

2

−2√3×

1

2

and Y = 4 sin 30° + 2√3 cos 30°
= 4×

1

2

+2√3×

√3

2

⇒ X = √3 and Y = 5
Hence, the given point in the new system is (√3,5).