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

1.	Find the Cartesian co-ordinates of points whose polar co-ordinates are: i. (3, 90°) ii. (1, 180°)
Answer» i. (r, θ) = (3, 90°) Using x = r cos θ and y = r sin θ, where (x, y) are the required cartesian co-ordinates, we get x = 3cos 90° and y = 3sin 90° ∴ x = 3(0) = 0 and y = 3(1) = 3 ∴ the required cartesian co-ordinates are (0, 3). ii. (r, θ) = (1, 180°) Using x = r cos θ and y = r sin θ, where (x, y) are the required cartesian co-ordinates, we get x = 1(cos 180°) and y = 1(sin 180°) ∴ x = -1 and y = 0 ∴ the required cartesian co-ordinates are (-1, 0).

Find the Cartesian co-ordinates of points whose polar co-ordinates are: i. (3, 90°) ii. (1, 180°)

Answer»

i. (r, θ) = (3, 90°)

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

x = 3cos 90° and y = 3sin 90°

∴ x = 3(0) = 0 and y = 3(1) = 3

∴ the required cartesian co-ordinates are (0, 3).

ii. (r, θ) = (1, 180°)

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

x = 1(cos 180°) and y = 1(sin 180°)

∴ x = -1 and y = 0

∴ the required cartesian co-ordinates are (-1, 0).