極座標 第十七單元

Polar Coordinate System

To plot points in Polar Coordinates

Relation to Cartesian Coordinates

Example

Find the Cartesian coordinates corresponding to ( 4, π/6 ) Solution:

Graphs of Polar Equations Cardioids and Limaçons 蚶

The Graph of Roses Polar equation of the form

The Graph of Spirals Spiral of Archimedes Logarithmic Spiral

Conchoid de Nicomedes

Conchoid de Nicomedes (graph)

Area of a Sector

Calculus in Polar Coordinates

Area in Polar Coordinates

Example Find the area of the region inside the limaçon

Solution

Arc Length

Arc Length(continued)

Arc Length Formula

Example

單元結語 還有很多以極座標方式表達的函數在此無 法一一列舉，同學可參考本校數學網站 再進入函數圖形。 以極座標方式有時比直角座標表示方便簡 捷很多。