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Evaluate Composite Trig Functions definitions

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  • Composite Function
    An expression where one function is applied inside another, requiring evaluation from the innermost to the outermost function.
  • Unit Circle
    A circle with radius 1 centered at the origin, used to determine trigonometric values for standard angles.
  • Right Triangle
    A triangle with one 90-degree angle, often used to solve trigonometric problems when unit circle values are unavailable.
  • Inverse Trig Function
    A function that returns the angle whose trigonometric value is a given number, with outputs restricted to specific intervals.
  • Interval
    The set of allowable angle values for an inverse trigonometric function, ensuring unique solutions.
  • Quadrant
    One of four sections of the coordinate plane, crucial for determining the sign and value of trigonometric functions.
  • Pythagorean Theorem
    A formula relating the sides of a right triangle, used to find missing side lengths when solving trigonometric problems.
  • Undefined Value
    A result that does not exist within the allowable range of a function, such as taking the inverse sine of a number outside [-1,1].
  • Argument
    The input value or expression inside a function, which determines the function's output.
  • SOHCAHTOA
    A mnemonic for remembering the ratios of sides in right triangle trigonometry: Sine, Cosine, and Tangent.
  • Hypotenuse
    The longest side of a right triangle, opposite the right angle, essential for calculating trigonometric ratios.
  • Adjacent Side
    The side next to the angle of interest in a right triangle, used in cosine and tangent calculations.
  • Opposite Side
    The side across from the angle of interest in a right triangle, used in sine and tangent calculations.
  • Principal Value
    The unique output of an inverse trigonometric function, determined by its restricted interval.
  • Cancellation Error
    A mistake made by assuming a trigonometric function and its inverse always undo each other, ignoring interval restrictions.