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Polar Coordinate System quiz

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  • In polar coordinates, what does the variable r represent?
    r represents the distance from the pole (origin) to the point.
  • How is the angle theta measured in the polar coordinate system?
    Theta is measured counterclockwise from the polar axis, which is equivalent to the positive x-axis.
  • What is the pole in the context of polar coordinates?
    The pole is the center point of the polar coordinate system, located at r = 0.
  • When plotting a point (r, θ) in polar coordinates, which value should you locate first?
    You should locate the angle theta first, then count r units from the pole.
  • How do you plot a point with a negative theta value in polar coordinates?
    A negative theta value means you measure the angle clockwise from the polar axis.
  • What should you do if the r value is negative when plotting a point in polar coordinates?
    If r is negative, count r units in the direction opposite to the angle theta.
  • How can multiple ordered pairs represent the same point in polar coordinates?
    By adding or subtracting multiples of 2π to theta or by changing r to negative and adding π to theta, you can get different pairs for the same point.
  • What is the effect of adding 2π to the angle theta in a polar coordinate pair?
    Adding 2π to theta results in the same direction, so the point remains unchanged.
  • If you change r to its negative value, what must you do to theta to represent the same point?
    You must add π to theta when you make r negative to represent the same point.
  • What is the ordered pair format for polar coordinates?
    Polar coordinates are written as (r, theta), where r is the radius and theta is the angle.
  • How do you find coterminal angles in polar coordinates?
    Coterminal angles are found by adding or subtracting multiples of 2π to the original angle theta.
  • What happens if you plot (r, θ) and (r, θ + 2πn) for any integer n?
    Both ordered pairs represent the same point in polar coordinates.
  • Why must you be careful when changing the sign of r in polar coordinates?
    Because you must also add π to theta to ensure the new pair represents the same point.
  • What does a negative r value indicate about the direction from the pole?
    A negative r value means you move in the direction opposite to the angle theta.
  • How can you verify that two polar coordinate pairs represent the same point?
    Plot both pairs on the polar grid and check if they end up at the same location.