Polar coordinates

Polar coordinates

Polar coordinates refer to a two-dimensional coordinate system that describes the position of a point by specifying its distance from an origin (known as the pole) and the angle between a line connecting the origin and the point and a given reference direction. The distance from the pole is represented as the first coordinate, while the angle from the reference direction is represented as the second coordinate.From: Mechanical Design for the Stage [2019], A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates [2020]

Geometry

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Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

Dan Zwillinger

In polar coordinates, the equation for a circle centered at the pole and having radius a is r = a. The equation for a circle of radius a passing through the pole and with center at the point (r,θ)=(a,θ0) $ (r, \theta ) = (a, \theta_{0} ) $ is r=2acos(θ-θ0) $ r = 2a {\text{cos }}(\theta - \theta_{0} ) $ . The equation for a circle of radius a and with center at the point (r,θ)=(r0,θ0) $ (r, \theta ) = (r_{0} , \theta_{0} ) $

Trigonometry and geometry

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Published in C.W. Evans, Engineering Mathematics, 2019

C.W. Evans

If that went well, then move ahead to step 4. Otherwise, try the next exercise. Remember that to transform from polar coordinates to cartesian coordinates we must use x = r cos θ and y = r sin θ. Once r and θ have been eliminated it is then just a question of identifying the curve.

A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates

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Journal Information

Published in International Journal of Mathematical Education in Science and Technology, 2020

Vahid Borji, Hedyeh Erfani, Vicenç Font

The polar coordinate system is defined as a two-dimensional coordinate system where each point on the plane has two indicators: a distance from the pole, , as the first coordinate and an angle from a reference direction, , as the second coordinate. In many of undergraduate courses, polar coordinate system is taught with a focus on geometric interpretations, conversions between polar and Cartesian coordinates and sketching polar graphs [1,4].

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Geometry

Trigonometry and geometry

A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates