Question

Find the polar co-ordinates of points whose Cartesian co-ordinates are:

`(- sqrt(3), 1)`

Answer 1

(x, y) = `(- sqrt(3), 1)`

∴ r = `sqrt(x^2 + y^2)`

= `sqrt(3 + 1)`

= `sqrt(4)`

= 2

tanθ = `y/x`

= `1/(-sqrt3)`

= `- tan  pi/6`

Since the given point lies in the 2^nd quadrant,

tanθ = `tan (pi - pi/6)`   ...[∵ tan (π – x) = – tan x]

∴ tanθ = `tan ((5pi)/6)`

∴ θ = `(5pi)/6` = 150°

∴ the required polar co-ordinates are (2, 150°).