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Phase Shifts definitions

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  • Phase Shift
    A horizontal translation of a sine or cosine graph, moving every point left or right by a specific amount.
  • Horizontal Shift
    A transformation that moves a graph along the x-axis, altering the starting position of its wave pattern.
  • Sine Function
    A periodic trigonometric function with a wave-like graph, starting at zero and oscillating between -1 and 1.
  • Cosine Function
    A periodic trigonometric function with a wave-like graph, starting at one and oscillating between -1 and 1.
  • Period
    The horizontal length required for a sine or cosine graph to complete one full cycle, calculated as 2π divided by b.
  • Amplitude
    The maximum vertical distance from the midline to the peak or trough of a sine or cosine graph.
  • h Value
    The constant added or subtracted inside the function, determining the amount and direction of the phase shift.
  • b Value
    The coefficient of x inside the function, affecting both the period and the calculation of the phase shift.
  • Wave Pattern
    The repeating up-and-down shape characteristic of sine and cosine graphs.
  • Transformation
    Any change to a graph's position, shape, or size, such as shifting, stretching, or compressing.
  • Trigonometric Function
    A function involving angles, commonly sine or cosine, that produces periodic wave-like graphs.
  • π (Pi)
    A mathematical constant approximately equal to 3.1416, often used to describe intervals and shifts in trigonometric graphs.
  • Full Period
    The interval over which a trigonometric graph completes one entire cycle before repeating.
  • Midline
    The horizontal axis that runs through the center of a sine or cosine graph, equidistant from its peaks and troughs.
  • Out of Phase
    A condition where two wave graphs have identical shapes but are horizontally shifted relative to each other.