Writing Parametric Equations definitions Flashcards
Writing Parametric Equations definitions
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Parametric Equations A pair of equations expressing x and y as functions of a third variable, often t, to describe a curve. Rectangular Equation An equation involving only x and y, representing a curve in the Cartesian plane without a parameter. Parameter An independent variable, typically denoted t, used to express both x and y in parametric equations. Domain Restriction A limitation on the set of allowable values for a variable, often caused by square roots or even powers. Pythagorean Identity The trigonometric relationship cos²(t) + sin²(t) = 1, used to parameterize circles and ellipses. Parameterization The process of expressing a rectangular equation as a set of parametric equations using a chosen parameter. Ellipse A curve described by an equation of the form ax² + by² = c, often parameterized with sine and cosine. Circle A special case of an ellipse where the coefficients of x² and y² are equal, parameterized using trigonometric functions. Cosine Function A trigonometric function commonly used in parameterizations to represent the x-component of circular or elliptical motion. Sine Function A trigonometric function often used in parameterizations to represent the y-component of circular or elliptical motion. Elimination of Parameter The process of removing the parameter from parametric equations to recover the original rectangular equation. Odd Power An exponent such as 1 or 3, preferred in parameter choices to avoid domain issues with negative values. Even Power An exponent such as 2 or 4, which can introduce domain restrictions when used in parameter choices. Function of t An expression where a variable, such as x or y, is written in terms of the parameter t. Substitution The act of replacing a variable in an equation with an equivalent expression, often used to derive y(t) from x(t).
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