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Graphs of Tangent and Cotangent Functions definitions

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  • Tangent Function
    A trigonometric curve formed by dividing sine values by cosine values, featuring vertical asymptotes and repeating every pi units.
  • Cotangent Function
    A reciprocal trigonometric curve of tangent, with vertical asymptotes at integer multiples of pi and a period matching tangent.
  • Asymptote
    A vertical line on a graph where the function approaches infinity, marking points of undefined values.
  • Period
    The horizontal distance on the x-axis after which a trigonometric curve repeats its shape.
  • Pi
    A mathematical constant representing the ratio of a circle’s circumference to its diameter, used to define periods and asymptote locations.
  • Transformation
    A modification applied to a function’s graph, such as shifting, stretching, or compressing, affecting its appearance but not its basic properties.
  • Reciprocal Identity
    A relationship where one trigonometric function is the inverse of another, such as cotangent being the reciprocal of tangent.
  • Odd Multiple
    A value obtained by multiplying pi/2 by an odd integer, indicating locations of tangent function asymptotes.
  • Integer Multiple
    A value obtained by multiplying pi by any whole number, marking cotangent function asymptote positions.
  • Curve Direction
    The orientation of a graph’s shape, with tangent rising from bottom left to top right and cotangent descending from top left to bottom right.
  • Undefined Value
    A point where division by zero occurs in a function, resulting in a gap or vertical asymptote on the graph.
  • X-Axis
    The horizontal axis on a graph, used to measure input values and locate periods and asymptotes.
  • Y-Axis
    The vertical axis on a graph, representing output values and points where the function reaches zero.
  • Cycle
    A complete segment of a repeating trigonometric graph, bounded by consecutive asymptotes.
  • B Value
    A coefficient affecting the period of a trigonometric function, determining how frequently the curve repeats.