Find the rectangular coordinates of a point P whose polar coordinates are (r, θ) = ( −2, 2π/3 ).

Question

Find the rectangular coordinates of a point P whose polar coordinates are (r, θ) = ( −2, 2π/3 ).

Express your final answer as an ordered pair (x, y).

Answer 1

To answer this question, we can recall our conversion factors for polar and rectangular coordinates: x = r cos(θ), and y = r sin(θ). We can then plug our values in to find our rectangular coordinates: y = r sin(θ) = -2 * sin(2π/3) = -2 * sqrt(3) / 2 = -sqrt(3). Similarly, we find that x = r cos(θ) = -2 * cos(2π/3) = -2 * -1/2 = 1. Therefore, we arrive at our rectangular coordinates of (x, y) = (1, -sqrt(3)).