Trigonometric Identities and Equations flashcards

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What is pythagorean relationships?Fundamental Trigonometric Identities: Equations relating squares of trigonometric functions on their common domains.
What condition or caution matters when using pythagorean relationships?Fundamental Trigonometric Identities: A squared value does not identify the sign of the original ratio.
What is quotients and valid cancellation?Fundamental Trigonometric Identities: Trig quotient rules combined with domain-preserving algebra.
What condition or caution matters when using quotients and valid cancellation?Fundamental Trigonometric Identities: Cancellation never restores an input excluded by the original denominator.
What is sum and difference formulas?Angle-Sum and Double-Angle Identities: Formulas evaluating trig functions of combined angles.
What condition or caution matters when using sum and difference formulas?Angle-Sum and Double-Angle Identities: Sine does not distribute over angle addition.
What is double-angle forms?Angle-Sum and Double-Angle Identities: Equivalent trig formulas for twice an angle.
What condition or caution matters when using double-angle forms?Angle-Sum and Double-Angle Identities: cos(2θ) generally differs from 2 cos θ.
What is roots on a specified interval?Solving Trigonometric Equations: Finding all angle inputs satisfying an equation within stated bounds.
What condition or caution matters when using roots on a specified interval?Solving Trigonometric Equations: The interval and its open or closed endpoints determine which roots count.
What is general solution families?Solving Trigonometric Equations: An integer-indexed description of all periodic equation roots.
What condition or caution matters when using general solution families?Solving Trigonometric Equations: A general solution must include negative as well as positive integer shifts.
What is zero-product method and lost roots?Factoring and Checking Trigonometric Equations: Solving a product equation by setting each factor equal to zero.
What condition or caution matters when using zero-product method and lost roots?Factoring and Checking Trigonometric Equations: Dividing by a variable trig factor can discard valid roots.
What is squared ratios and both signs?Factoring and Checking Trigonometric Equations: Recovering both sign possibilities from a squared trig value.
What condition or caution matters when using squared ratios and both signs?Factoring and Checking Trigonometric Equations: Taking only the positive square root loses negative-ratio solutions.