Question

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

(–1, –1)

Answer 1

Here, x = – 1 and y = – 1

∴ the point lies in the third quadrant.

Let the polar coordinates be (r, θ)

∴ r² = x² + y² = ( – 1)² + ( – 1)² = 1 + 1 = 2

∴ r = `sqrt(2)`    ...[∵ r > 0]

tanθ = `y/x = (-1)/(-1)` = 1

Since the point lies in the third quadrant and 0 ≤ θ < 2π,

tanθ = 1

= tan 45°

= tan (180° + 45°) ...[∵ tanθ is periodic function with period π = 180°]

∴ tanθ = tan225°

∴ θ = 225°

∴ the polar coordinates of the given point are `(sqrt(2), 225^circ)`.