“Polar Coordinates”的概念、定义、习题解题方法及翻译-数学辞典

单词

Polar Coordinates

释义

Polar Coordinates

The polar coordinates and are defined by

			(1)
			(2)

In terms of

and

			(3)
			(4)

The Arc Length of a polar curve given by

(5)

The Line Element is given by

(6)

and the Area element by

(7)

The Area enclosed by a polar curve

(8)

The Slope of a polar function

at the point

is given by

(9)

The Angle between the tangent and radial line at the point

(10)

A polar curve is symmetric about the

-axis if replacing

in its equation produces an equivalentequation, symmetric about the

-axis if replacing

in its equation produces an equivalentequation, and symmetric about the origin if replacing

in its equation produces an equivalent equation.

In Cartesian coordinates, the Position Vector and its derivatives are

In polar coordinates, the Unit Vectors and their derivatives are

See also Cardioid, Circle, Cissoid, Conchoid, Curvilinear Coordinates, CylindricalCoordinates, Equiangular Spiral, Lemniscate, Limaçon, Rose

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