Find all polar coordinates of point P where P = ordered pair 3 comma negative pi divided by 3 .

Answer:The all polar coordinates of P are:(3 , -π/3) , (3 , 5π/3) , (-3 , 2π/3) , (-3 , -4π/3)Step-by-step explanation:* Lets study the polar coordinates of a point- In polar coordinates there is an infinite number of coordinates  for a given point. - The polar coordinates of a point (x , y) is (r , θ), where   r = √ ( x2 + y2 )   θ = tan-1 ( y / x )# Ex: the following four points are all coordinates for the same point.* (5 , π/3) = (5 , −5π/3) = (−5 , 4π/3) =(−5 , −2π/3) - These four points only represent the coordinates of the point without     rotating more than once- So the point (r,θ) can be represented by any of the following   coordinate pairs  (r , θ + 2π n) and (−r , θ + (2n + 1) π), where n is   any integer.* Now lets solve the problem∵ P = (3 , -π/3)∵ (r , θ + 2πn)∴ r = 3 an d Ф = -π/3- let n = 1∴ P = (3 , -π/3 + 2π)∴ P = (3 , 5π/3)∵ P =(3 , -π/3)∵ P = (-r , θ + (2n + 1) π)Let n = 0∴ P = (-3 , -π/3 + (2×0 + 1) π)∴ P = (-3 , -π/3 + (0 + 1) π)∴ P = (-3 , -π/3 + π)∴ P = (-3 , 2π/3)∵ P =(3 , -π/3)∵ P = (-r , θ + (2n + 1) π)Let n = -1∴ P = (-3 , -π/3 + (2(-1) + 1) π) ∴ P = (-3 , -π/3 + (-2 + 1) π)∴ P = (-3 , -π/3 + -π) = (-3 , -4π/3)∴ P = (-3 , -4π/3)