PPT-Polar Coordinates

MATH 1112 S F Ellermeyer Rectangular vs Polar Coordinates Rectangular coordinates are the usual xy coordinates Polar coordinates are r θ coordinates where θ is the directed angle measured in the usual way and r is the directed distance from the origin to the point in question Directed distance means that we travel in the direction of the terminal side of . Butthere isanotherwaytospecifythepositionofapointandthatist ousepolarcoordinates r In thisunitweexplainhowtoconvertfromCartesiancoordina testopolarcoordinatesandback again Inordertomasterthetechniquesexplainedhereitisvitalt hatyouundertakeplentyofpr If ab be a continuous function and 0 then the area of the region between the graph of and the xaxis is de64257ned to be Area dx Instead of the xaxis we can take a graph of another continuous function such that for all ab and de64257ne the area o It is important to remember that expressions for the operations of vector analysis are different in di64256erent coordinates Here we give explicit formulae for cylindrical and spherical coordinates 1 Cylindrical Coordinates In cylindrical coordinate a In polar coordinates what shapes are described by and where is a constant Solution describes a circle of radius centered at the origin describes a ray from the origin which makes an angle of when measured counterclockwise from the axis b Draw 0 Coordinate Systems. Representing 3D points in Cylindrical Coordinates. . . r. Start from polar . representations in the plane. Representing 3D points in Cylindrical Coordinates. . . r. Cylindrical coordinates just adds a . thermal$ stable Both the Southern the Southern almost exclusively ice). A September and the sea even at mer minimum surface (roughly km?) remains ice-covered. the sea-ice cover much less the Southern Vectors in three space. Team 6:. Bhanu Kuncharam. Tony Rocha-. Valadez. Wei Lu. The position vector . R. from the origin of . Cartesian coordinate system. to the point (x(t), y(t), z(t)) is given by the expression. Part I: Polar Coordinates. Objectives. Objectives: Know how to convert between polar and Cartesian coordinates and how to sketch functions in polar coordinates. Corresponding Sections in Simmons 16.1,16.2,16.3. Gra. ph the set of points whose polar coordinates satisfy the. g. iven equations and inequalities.. Relating Polar and Cartesian Coordinates. Section 10.5b. Relating Polar and Cartesian Coordinates. Coordinate Conversion. Exponent. Logarithm. Curves . theory. Graphing . functions. Polar . coordinates. Mid-Term Exam . preparation. Mid-Term Exam preparation. studying mostly numbers, graphs, limits, continuity, derivative and integral. Introduction. Polar coordinates are an alternative system to Cartesian coordinates. Some processes and equations involving the Cartesian system can become very complicated. You can simplify some of these by using Polar coordinates instead. Parabola: the collection of all points that are equidistant from a point(focus) and a line(. directrix. ). 1. Distance from A to focus:. Distance from B to focus:. Distance from C to focus:. 2. Vertex at. Polar coordinates are an alternative system to Cartesian coordinates. Some processes and equations involving the Cartesian system can become very complicated. You can simplify some of these by using Polar coordinates instead. Change coordinate system so that center of the coordinate system is at pinhole and Z axis is along viewing direction. Perspective projection. The projection equation. Is this equation linear?. Can this equation be represented by a matrix multiplication?.