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Inverse Sine, Cosine, & Tangent definitions Flashcards

Inverse Sine, Cosine, & Tangent definitions
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  • Inverse Trig Function
    Mathematical operation that retrieves an angle from a given trigonometric value, effectively reversing the original trig function.
  • Inverse Cosine
    Function that returns an angle in the interval [0, π] whose cosine equals a specified value between -1 and 1.
  • Inverse Sine
    Function that yields an angle in the interval [-π/2, π/2] whose sine matches a given value between -1 and 1.
  • Inverse Tangent
    Function that provides an angle in the interval [-π/2, π/2] whose tangent equals any real number input.
  • Unit Circle
    Circle with radius 1 centered at the origin, used to relate angles to trigonometric values for both standard and inverse functions.
  • Interval
    Specific range of angle values where an inverse trig function is defined and produces unique outputs.
  • Quadrant
    One of four sections of the coordinate plane, used to determine the sign and value of trigonometric functions.
  • Radian
    Unit of angular measure based on arc length, commonly used for expressing angles in trigonometric contexts.
  • Vertical Line Test
    Graphical method for determining if a curve represents a function by checking if any vertical line crosses it more than once.
  • One-to-One Function
    Type of function where each input corresponds to exactly one output, necessary for defining an inverse.
  • Reflection
    Transformation that flips a graph over a line, such as y = x, to produce the graph of an inverse function.
  • Domain
    Set of all possible input values for a function, such as the allowed values for inverse trig functions.
  • Range
    Set of all possible output values for a function, particularly the angle intervals for inverse trig functions.
  • Calculator Mode
    Setting that determines whether a calculator interprets angles in degrees or radians when evaluating trig functions.
  • Specified Interval
    Restricted set of angle values used to ensure inverse trig functions yield unique solutions.