Final answer:
To plot the point with polar coordinates (-2, -4π), we convert it to Cartesian coordinates. The point is (-2, 0). Other polar coordinate representations are (-2, 0) for r < 0 and (2, -4π) for r > 0.
Step-by-step explanation:
To plot a point with given polar coordinates (-2, -4π), we need to convert it to Cartesian coordinates.
The Cartesian coordinates can be found using the formulas:
x = r * cosθ and y = r * sinθ
Plugging in the values, we get:
x = -2 * cos(-4π) and y = -2 * sin(-4π)
Simplifying the equations, we find that x = -2 and y = 0.
So, the point with the given polar coordinates is (-2, 0).
For two other polar coordinate representations, we can consider r with a negative value and a positive value:
The point with r < 0 can be represented as (-|-2|, -4π), which is (-2, 0)
The point with r > 0 can be represented as (|-2|, -4π), which is (2, -4π)