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Graphs of Trigonometric Functions definitions

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  • Unit Circle
    A circle with radius 1, used to determine sine and cosine values based on x and y coordinates.
  • Crest
    A highest point on a wave-like graph, representing the maximum output value.
  • Trough
    A lowest point on a wave-like graph, representing the minimum output value.
  • Vertical Shift
    A transformation that moves a graph up or down by adding a constant to the function.
  • Reciprocal Identity
    A relationship where one trigonometric function equals 1 divided by another, such as cosecant and sine.
  • Asymptote
    A vertical line where a graph approaches infinity due to division by zero, indicating undefined values.
  • Period
    The horizontal length required for a trigonometric graph to complete one full cycle and start repeating.
  • Peak
    A point on a graph where the function reaches its highest value within a cycle.
  • Valley
    A point on a graph where the function reaches its lowest value within a cycle.
  • Transformation
    A change applied to a graph, such as shifting or stretching, altering its position or shape.
  • Secant
    A trigonometric function defined as the reciprocal of cosine, with its own distinct graph and asymptotes.
  • Cosecant
    A trigonometric function defined as the reciprocal of sine, featuring vertical asymptotes at sine's zeros.
  • Tangent
    A trigonometric function formed by dividing sine by cosine, with a period of π and vertical asymptotes.
  • Cotangent
    A trigonometric function formed as the reciprocal of tangent, with a period of π and shifted asymptotes.
  • Wave Pattern
    A repeating, oscillating shape seen in sine and cosine graphs, characterized by regular crests and troughs.