Parametric equations can describe complicated curves that are difficult or perhaps impossible to describe using rectangular coordinates Parametric equations provide a convenient way to describe a curve.

A parameter can represent time or some other meaningful quantity It is often possible to eliminate the parameter in a parameterized curve to obtain a function or relation describing that curve

parametric equations — the equations x = x ( t ) and y = y ( t ) that define a parametric curve. angular coordinate — θ the angle formed by a line segment connecting the origin to a point in the polar coordinate system with the positive radial ( x ) axis, measured counterclockwise. parameter — an independent variable that both x and y depend on in a parametric curve; usually represented by the variable t. parametric curve — the graph of the parametric equations x ( t ) and y ( t ) over an interval a ≤ t ≤ b combined with the equations.

Be able to convert points between rectangular and polar coordinates using the formulas x = r cos θ and y = r sin θ and r = x 2 + y 2 and tan θ = y x; use the conversion formulas to convert equations between rectangular and polar coordinates; identify symmetry in polar curves, which can occur through the pole, the horizontal axis, or the vertical axis.