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Graphs of Tangent and Cotangent Functions definitions Flashcards

Graphs of Tangent and Cotangent Functions definitions
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  • Tangent Function
    A trigonometric function defined as the ratio of sine to cosine, with a graph featuring repeating curves and vertical asymptotes.
  • Cotangent Function
    A trigonometric function that is the reciprocal of tangent, with a graph that is a flipped version of the tangent graph.
  • Asymptote
    A vertical line on a graph where the function approaches infinity or is undefined, often due to division by zero.
  • Period
    The horizontal distance required for a function's graph to complete one full cycle before repeating.
  • Odd Multiple of π/2
    Values like π/2, 3π/2, etc., where the tangent function has vertical asymptotes due to cosine equaling zero.
  • Integer Multiple of π
    Values like 0, π, 2π, etc., where the cotangent function has vertical asymptotes due to sine equaling zero.
  • Reciprocal Identity
    A relationship where one trigonometric function is the reciprocal of another, such as cotangent being one over tangent.
  • Transformation
    A change applied to a function's graph, such as shifting, stretching, or compressing, affecting its appearance.
  • Zero
    A point on the graph where the function's output is exactly zero, often corresponding to x-intercepts.
  • Vertical Stretch
    A transformation that increases the steepness of a graph, making its curves rise or fall more sharply.
  • Horizontal Shift
    A transformation that moves the entire graph left or right along the x-axis.
  • Undefined Value
    A point where the function cannot be evaluated, typically due to division by zero, resulting in an asymptote.
  • Repeating Behavior
    A property where a function's graph repeats its pattern at regular intervals along the x-axis.
  • Curve Orientation
    The direction in which a graph's curve moves between asymptotes, such as bottom-left to top-right or top-left to bottom-right.
  • X-Intercept
    A point where the graph crosses the x-axis, indicating the input value for which the function's output is zero.