To plot the point given in polar coordinates, we start with the values provided: the radius is 3 and the angle is 3π/2.
In polar coordinates, the general form is (r, θ), where r represents the distance from the origin and θ represents the angle measured from the positive x-axis. The angle 3π/2 radians corresponds to 270 degrees, which points directly downward along the negative y-axis.
Now, to find the Cartesian coordinates (x, y), we use the conversion formulas:
- x = r * cos(θ)
- y = r * sin(θ)
Substituting in our values:
- x = 3 * cos(3π/2) = 3 * 0 = 0
- y = 3 * sin(3π/2) = 3 * (-1) = -3
Thus, the Cartesian coordinates of the point are (0, -3).