Parametric Equations and Polar Coordinates

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Key Terms

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Key Terms

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.

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