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Graphs of the Sine and Cosine Functions definitions

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  • Unit Circle
    A circle with radius 1 centered at the origin, used to define sine and cosine values based on coordinates.
  • Wave Pattern
    A repeating, smooth curve seen in sine and cosine graphs, resulting from their cyclical nature.
  • Crest
    The highest point reached by the graph of a wave, also called a peak.
  • Trough
    The lowest point reached by the graph of a wave, also called a valley.
  • Amplitude
    The distance from the midline to a peak or trough, indicating the height of the wave.
  • Midline
    A horizontal line that runs through the center of a wave, equidistant from crests and troughs.
  • Vertical Shift
    A transformation that moves the entire graph up or down by adding a constant to the function.
  • Reflection
    A transformation that flips the graph over the x-axis, caused by a negative multiplier.
  • Period
    The horizontal length required for a wave to complete one full cycle on the x-axis.
  • Cycle
    A complete sequence of values in a wave, starting and ending at the same point on the graph.
  • Coefficient
    A number multiplying the variable inside the function, affecting the period or amplitude.
  • 2π
    The standard period for basic sine and cosine functions, representing one full rotation around the unit circle.
  • Horizontal Stretch
    A transformation that widens the graph, occurring when the coefficient of x is between 0 and 1.
  • Horizontal Shrink
    A transformation that compresses the graph, occurring when the coefficient of x is greater than 1.
  • Peak
    A point on the graph where the function reaches a local maximum, synonymous with crest.