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Phase Shifts quiz

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  • What is a phase shift in the context of sine and cosine graphs?
    A phase shift is a horizontal shift of the sine or cosine graph, moving it left or right.
  • How does subtracting a number from x inside a sine or cosine function affect the graph?
    Subtracting a number from x shifts the graph to the right by that amount.
  • How does adding a number to x inside a sine or cosine function affect the graph?
    Adding a number to x shifts the graph to the left by that amount.
  • What is the general formula to determine the amount of phase shift in y = sin(bx ± h) or y = cos(bx ± h)?
    The phase shift is h divided by b, or h/b.
  • If you have y = cos(x - π/2), how is the graph shifted?
    The graph is shifted to the right by π/2 units.
  • What is the period of a sine or cosine function y = sin(bx) or y = cos(bx)?
    The period is 2π divided by b, or 2π/b.
  • For y = sin(2x + π), in which direction and by how much is the graph shifted?
    The graph is shifted to the left by π/2 units.
  • How can a phase shift make a cosine graph resemble a sine graph?
    A phase shift can align the peaks and zeros of the cosine graph with those of the sine graph, making them look similar.
  • What does the value of b in y = sin(bx ± h) or y = cos(bx ± h) affect?
    The value of b affects the period of the graph.
  • If the inside of the function is bx - h, which direction does the graph shift?
    The graph shifts to the right by h/b units.
  • If the inside of the function is bx + h, which direction does the graph shift?
    The graph shifts to the left by h/b units.
  • How do you rewrite y = sin(2x + π) to make the phase shift more apparent?
    You can rewrite it as y = sin[2(x + π/2)], showing a shift left by π/2 units.
  • What happens to the starting point of the graph when a phase shift is applied?
    The starting point moves horizontally by the phase shift amount.
  • Why is understanding phase shifts important when graphing trigonometric functions?
    Understanding phase shifts helps accurately graph and analyze the behavior of sine and cosine functions.
  • What is the effect of the coefficient b on the graph of y = sin(bx) or y = cos(bx)?
    The coefficient b changes the period of the graph, making it stretch or compress horizontally.