Find the Rectangular Coordinates of the Point with the Polar Coordinates 3 and 3π/2

To convert polar coordinates to rectangular coordinates, we can use the formulas:

• x = r * cos(θ)
• y = r * sin(θ)

Here, the polar coordinates given are (r, θ) = (3, 3π/2). In this case, r = 3 and θ = 3π/2 radians.

Now, we calculate the x and y coordinates:

• x = 3 * cos(3π/2)
• y = 3 * sin(3π/2)

We know that:

• cos(3π/2) = 0
• sin(3π/2) = -1

Substituting these values in, we get:

• x = 3 * 0 = 0
• y = 3 * (-1) = -3

Therefore, the rectangular coordinates are (0, -3).