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Introduction to Trigonometric Identities definitions

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  • Even Function
    Symmetry about the y-axis; output remains unchanged when input sign is flipped.
  • Odd Function
    Symmetry about the origin; output sign reverses when input sign is flipped.
  • Cosine
    Trigonometric function classified as even; value unchanged for negative angles.
  • Sine
    Trigonometric function classified as odd; value negated for negative angles.
  • Tangent
    Trigonometric function classified as odd; value negated for negative angles.
  • Secant
    Reciprocal of cosine; classified as even, unchanged for negative angles.
  • Cosecant
    Reciprocal of sine; classified as odd, negated for negative angles.
  • Cotangent
    Reciprocal of tangent; classified as odd, negated for negative angles.
  • Identity
    Equation true for all possible values of its variable, used to simplify expressions.
  • Even-Odd Identity
    Rule for replacing trigonometric functions of negative angles based on function symmetry.
  • Pythagorean Identity
    Relationship among squared sine, cosine, tangent, secant, cotangent, and cosecant values.
  • Argument
    Input value inside parentheses of a trigonometric function, often an angle.
  • Simplification
    Process of rewriting expressions with positive arguments, fewer functions, and no fractions.
  • Verification
    Demonstration that both sides of a trigonometric equation are equal using identities.
  • Unit Circle
    Circle with radius one, used to define trigonometric function values for specific angles.