Question

If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.

पर्याय

• `(1, (4pi)/3)`

• `(2, (3pi)/4)`

• `(3, (7pi)/4)`

• `(4, (5pi)/4)`

Answer 1

If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are `(2, (3pi)/4)`.

Explanation:

We have, r cos θ = - `sqrt2` and r sin θ = `sqrt2`

∴ r² cos² θ + r² sin² θ = 2 + 2 = 4

⇒ r²(cos² θ + sin² θ) = 4

⇒ r = ± 2 and θ = `tan^-1 (sqrt2/(- sqrt2))`

θ = tan^-1 (- 1) ⇒ θ = `(3pi)/4`

∴ Required polar co-ordinate is (r, θ)

`= (2, (3pi)/4)`