Parametric Equations and Polar Coordinates

Limacon  -  A polar equation of the form r = a + b sin(θ) or r = a + b cos(θ) , where a, b≠ 0 .

Logarithmic Spiral  -  A polar equation of the form r = ab ^θ .

Orientation  -  The direction of a plane curve as the parameter increases.

Parameter  -  A third variable (often time) which determines the values of x and y in parametric equations.

Parametric Equations  -  Two equations of the form x = f (t) and y = g(t) , which specify the location of a point according to the variable t .

Plane Curve  -  The set of all points (f (t), g(t)) , where x = f (t) and y = g(t) are parametric equations.

Polar Axis  -  The ray whose endpoint is the pole and which is the initial side of any angle measure in the polar plane.

Polar Coordinate System  -  The system in which a point in the plane is specified according to an ordered pair (r, θ) in which r is a length and θ is an angle. The length r refers to the distance from the point to a fixed origin, called the pole. The angle θ is the angle whose initial side is a fixed ray (the polar axis) and whose terminal side contains the point. Under these circumstances, the point (r, θ) is expressed in polar coordinates.

Pole  -  The fixed point in the polar coordinate system from which every point is r units away.

Rectangular Coordinate System  -  The coordinate system in which every point is specified by exactly one ordered pair (x, y) . Here x is the distance between the point and a fixed line (the y -axis) and y is the distance between the point and a line fixed perpendicular to the other line (this line is the x -axis). The perpendicular lines are the axes, and the point (x, y) is expressed in rectangular coordinates.

Rose Curve  -  A polar equation of the form r = a sin(nθ) or r = a cos(nθ) , where n is an integer.

Spiral of Archimedes  -  A polar equation of the form r = aθ + b .