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Introduction to Trigonometric Identities definitions

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  • Even Function
    A function whose graph is symmetric about the y-axis, producing identical outputs for positive and negative inputs.
  • Odd Function
    A function whose graph is symmetric about the origin, with outputs for negative inputs being the negatives of those for positive inputs.
  • Argument
    The value or expression inside the parentheses of a trigonometric function, such as the angle in sine or cosine.
  • Pythagorean Identity
    An equation relating squared trigonometric functions, derived from the Pythagorean theorem, true for all angle values.
  • Unit Circle
    A circle with radius one, centered at the origin, used to define trigonometric function values for all angles.
  • Difference of Squares
    An algebraic pattern where the product of a sum and difference yields the difference between two squares.
  • Secant
    A trigonometric function defined as the reciprocal of cosine, often used in identities and simplifications.
  • Cosecant
    A trigonometric function defined as the reciprocal of sine, appearing in various trigonometric identities.
  • Cotangent
    A trigonometric function defined as the ratio of cosine to sine, or the reciprocal of tangent.
  • Identity
    An equation involving trigonometric functions that holds true for all permissible values of the variables involved.
  • Simplification
    The process of rewriting a trigonometric expression to have positive arguments, no fractions, and the fewest functions possible.
  • Verification
    The process of demonstrating that both sides of a trigonometric equation are equal by applying identities and simplification.
  • Reciprocal Function
    A trigonometric function that is the inverse of another, such as secant for cosine or cosecant for sine.
  • Squared Trigonometric Function
    A trigonometric function raised to the second power, commonly appearing in Pythagorean identities.
  • Symmetry
    A property of a function's graph indicating invariance under certain transformations, such as reflection about the y-axis or origin.