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Phase Shifts quiz

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  • What is a phase shift in trigonometric functions?
    A phase shift is a horizontal shift of the graph of a sine or cosine function, moving it left or right.
  • How do you identify a phase shift in a sine or cosine function?
    A phase shift occurs when a constant is added or subtracted inside the function's argument, such as in sine(x - h) or cosine(x + h).
  • What is the formula to calculate the magnitude of a phase shift?
    The magnitude of a phase shift is given by h/b, where h is the phase shift constant and b is the coefficient of x.
  • If you have cosine(x - pi/2), in which direction and by how much is the graph shifted?
    The graph is shifted to the right by pi/2 units.
  • What happens to the graph when you subtract a positive number inside the function's argument?
    Subtracting a positive number shifts the graph to the right by that amount divided by the coefficient of x.
  • How does adding a number inside the function's argument affect the graph?
    Adding a number shifts the graph to the left by the value of the number divided by the coefficient of x.
  • What is the effect of the coefficient 'b' in the phase shift formula h/b?
    The coefficient 'b' scales the phase shift, so the actual shift is h divided by b.
  • How can a phase shift make a cosine graph resemble a sine graph?
    A phase shift can align the starting points and peaks of the cosine graph with those of the sine graph, making them look similar.
  • What is the period of the function y = sin(2x)?
    The period is pi, calculated as 2pi divided by the coefficient 2.
  • For y = sin(2x + pi), what is the phase shift and in which direction?
    The phase shift is pi/2 units to the left.
  • How do you graph a sine or cosine function with a phase shift?
    Adjust the starting point and subsequent points by the phase shift, then connect these points smoothly to form the new wave.
  • If the inside of the function is bx - h, what is the direction of the phase shift?
    The graph shifts to the right by h/b units.
  • If the inside of the function is bx + h, what is the direction of the phase shift?
    The graph shifts to the left by h/b units.
  • Why might different textbooks use different letters for the phase shift constant?
    Different textbooks may use different variables, but the concept remains the same as long as a constant is added or subtracted inside the function.
  • How can rewriting y = sin(2x + pi) as y = sin[2(x + pi/2)] help with graphing?
    It makes it clear that the graph is shifted left by pi/2 units, helping to visualize the transformation.