Question

Find the polar coordinates of points whose cartesian coordinates are:

(5, 5)

Answer 1

Here, x = 5 and y = 5

∴ The point lies in the first quadrant

Let the polar coordinates be (r, θ)

∴ r² = x² + y² = 5² + 5² = 25 + 25 = 50

∴ r = `5sqrt(2)`   ...[∵ r > 0]

tanθ = `y/x = 5/5` = 1

Since the point lies in the first quadrant and

0 ≤ θ < 2π, tanθ = 1 = tan45°

∴ θ = 45°

∴ the polar coordinates of the given point are `(5sqrt(2),  45^circ)`.