secant

(noun)

a straight line that intersects a curve at two or more points

Related Terms

  • tangent
  • mean

Examples of secant in the following topics:

  • The Mean Value Theorem, Rolle's Theorem, and Monotonicity

    • In calculus, the mean value theorem states, roughly: given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints .
    • For any function that is continuous on $[a, b]$ and differentiable on $(a, b)$ there exists some $c$ in the interval $(a, b)$ such that the secant joining the endpoints of the interval $[a, b]$ is parallel to the tangent at $c$.
  • Trigonometric Functions

    • The sine, tangent, and secant functions of an angle constructed geometrically in terms of a unit circle.
  • Hyperbolic Functions

  • The Derivative and Tangent Line Problem

    • The slope of the secant line passing through $p$ and $q$ is equal to the difference quotient
  • Limit of a Function

    • It also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.
  • Trigonometric Integrals

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