Question

Find the Cartesian co-ordinates of point whose polar co-ordinates are `(4, pi/3)`

Answer 1

(r, θ) = `(4, pi/3)`

Using x = r cos θ and y = r sin θ, where (x, y) are the required Cartesian co-ordinates, we get

x = `4 cos (pi/3)` and y = `4 sin (pi/3)`

∴ x = `4(1/2)` and y = `4(sqrt(3)/2)`

∴ x = 2 and y = `2sqrt(3)`

∴ The required Cartesian co-ordinates are `(2, 2sqrt(3))`.