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Inverse Sine, Cosine, & Tangent definitions

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  • Inverse Trigonometric Function
    Returns an angle whose trigonometric value matches a given input, with domain and range restrictions for each function.
  • Inverse Cosine
    Yields an angle between 0 and pi for input values from -1 to 1, reflecting the cosine graph over y = x within this interval.
  • Inverse Sine
    Produces an angle between -pi/2 and pi/2 for input values from -1 to 1, reflecting the sine graph over y = x in this range.
  • Inverse Tangent
    Provides an angle between -pi/2 and pi/2 for any real input, reflecting the tangent graph over y = x within this interval.
  • Unit Circle
    A circle with radius 1 used to identify angles and their corresponding trigonometric values for evaluating inverse functions.
  • Interval
    A specific range of angles or values where an inverse trigonometric function is defined and yields valid results.
  • Domain
    The set of input values allowed for an inverse trigonometric function, often restricted to ensure a unique output.
  • Range
    The set of possible output angles for an inverse trigonometric function, determined by the function's definition.
  • Reflection
    A transformation of a trigonometric graph over the line y = x to create its inverse, limited to a one-to-one segment.
  • Vertical Line Test
    A method to determine if a graph represents a function, ensuring each input yields only one output.
  • Quadrant
    A section of the unit circle used to locate angles and values, relevant for identifying valid solutions in inverse functions.
  • Radian Mode
    A calculator setting for measuring angles in radians, commonly used when evaluating inverse trigonometric functions.
  • Second Function Key
    A calculator button used to access inverse trigonometric functions, such as inverse sine, cosine, or tangent.
  • One-to-One Function
    A function where each input corresponds to a unique output, necessary for defining an inverse function.
  • Specified Interval
    The exact range of angles considered valid for an inverse trigonometric function, ensuring correct solutions.