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Defining the Unit Circle quiz

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  • What is the radius of the unit circle?
    The radius of the unit circle is 1.
  • What is the equation of the unit circle centered at the origin?
    The equation is x² + y² = 1.
  • What are the degree measures for a full rotation around the unit circle?
    A full rotation is 360 degrees.
  • What are the radian measures for a full rotation around the unit circle?
    A full rotation is 2π radians.
  • What (x, y) coordinate corresponds to 0 degrees on the unit circle?
    The coordinate is (1, 0).
  • What (x, y) coordinate corresponds to 90 degrees on the unit circle?
    The coordinate is (0, 1).
  • What (x, y) coordinate corresponds to 180 degrees on the unit circle?
    The coordinate is (-1, 0).
  • What (x, y) coordinate corresponds to 270 degrees on the unit circle?
    The coordinate is (0, -1).
  • How do you verify if a point lies on the unit circle?
    Plug the point's x and y values into x² + y² and check if the result equals 1.
  • Is the point (1, 1) on the unit circle? Why or why not?
    No, because 1² + 1² = 2, which does not equal 1.
  • Is the point (1/2, √3/2) on the unit circle? Why or why not?
    Yes, because (1/2)² + (√3/2)² = 1/4 + 3/4 = 1.
  • To what angle does the point (1/2, √3/2) correspond on the unit circle?
    It corresponds to 60 degrees.
  • Where is the center of the unit circle located on the coordinate plane?
    The center is at the origin, (0, 0).
  • What is the radian measure for 90 degrees?
    90 degrees is π/2 radians.
  • What is the radian measure for 180 degrees?
    180 degrees is π radians.