Question

Given the polar coordinates (-2, 3pi/2), which of the following rectangular coordinate pairs represents the same point?

A. (0,-2)
B. (2,0)
C.(0,2)
D.(-2,0)

Answer 1

polar coordinates (r, a)
"a" is angle in radians

x = rcos(a)
y = rsin(a)

use the given values.

x = -2cos(3pi/2)
x = 0

y = -2sin(3pi/2)
y = 2

C. (0,2)

Answer 2

C.(0,2) rectangular coordinate pairs represents the same point.

Explanation:

Given : polar coordinates (-2, 3pi/2).

To find : which of the following rectangular coordinate pairs represents the same point.

Solution : We have given that polar coordinates (-2, 3pi/2).

Polar coordinates : is a two-dimensional system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction ( r , Ф)

Here, r = -2 , Ф = 3pi/2

Representation of polar coordinates :

x = r cosФ.

Plugging the values of r and Ф

x = -2 cos( 3 pi/2)

x = 0

y = r sinФ

Plugging the values or r and Ф

y = -2 sin(3pi/2)

y = -2 (-1)

y = 2

Coordinates (x, y) = (0 ,2)

Therefore, C.(0,2) rectangular coordinate pairs represents the same point.