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Graphs of the Sine and Cosine Functions quiz

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  • What coordinate on the unit circle is associated with the sine function?
    The sine function is associated with the y-coordinate on the unit circle.
  • What coordinate on the unit circle is associated with the cosine function?
    The cosine function is associated with the x-coordinate on the unit circle.
  • What is the general shape of the graphs of sine and cosine functions?
    Both sine and cosine graphs have a repeating wave pattern.
  • Where does the graph of y = sin(x) start on the y-axis?
    The graph of y = sin(x) starts at 0 on the y-axis.
  • Where does the graph of y = cos(x) start on the y-axis?
    The graph of y = cos(x) starts at 1 on the y-axis.
  • What are the high points and low points of a sine or cosine wave called?
    High points are called peaks or crests, and low points are called valleys or troughs.
  • What effect does adding a constant k to y = sin(x) or y = cos(x) have on the graph?
    Adding a constant k shifts the graph vertically; positive k shifts up, negative k shifts down.
  • How would the graph of y = sin(x) + 1 differ from y = sin(x)?
    The graph of y = sin(x) + 1 is shifted up by 1 unit compared to y = sin(x).
  • What is the amplitude of y = sin(x) or y = cos(x)?
    The amplitude is 1 for both y = sin(x) and y = cos(x).
  • How do you change the amplitude of a sine or cosine graph?
    Multiply the function by a number; the amplitude becomes the absolute value of that number.
  • What happens to the graph if the amplitude is negative?
    A negative amplitude reflects the graph over the x-axis.
  • What is the period of y = sin(x) or y = cos(x)?
    The period is 2π for both y = sin(x) and y = cos(x).
  • How does the period change for y = sin(2x)?
    The period becomes π, which is half the original period.
  • What is the formula for the period of y = sin(Bx) or y = cos(Bx)?
    The period is calculated as 2π divided by B, where B is the coefficient of x.
  • If y = cos(4πx), what is the period of the function?
    The period is 1/2, calculated as 2π divided by 4π.