Parametric equations define a set of related quantities as explicit functions of an independent parameter, often denoted as $t$. These equations are commonly used to describe curves and motion in the plane.
5 Must Know Facts For Your Next Test
Parametric equations for a curve generally consist of two functions: $x(t)$ and $y(t)$.
The parameter $t$ often represents time, but can represent any other variable.
You can convert parametric equations into a single Cartesian equation by eliminating the parameter $t$.
The derivatives $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are used to find the slope of the tangent line to the curve at any point.
The arc length of a curve defined by parametric equations can be found using $$\int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt$$.