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) ,0)

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

Step-by-step 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.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!