Calculus2.2

Calculus2.2 - Section 6.3: Polar Forms & Area Polar...

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Section 6.3: Polar Forms & Area

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Rectangular coordinates were horizontal/vertical directions for reaching the point Eg: 3, in polar 4    Polar coordinates are "as the crow flies"directions (x,y) 4 3 cos , 3 x so  22 1 x = r cos y = r sin tan x y r y x   Polar Coordinates:
Notation 4 3, 3 3cis 3e 4 4 4 i      , r rcis re i r Warnings 59 3, and and 4 4 4 Same point   0, is always the origin

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Graph r = 3 = 4
Graph r =

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Graph r = 4 sin r θ sin
Graph r = 4 sin r θ 0 sin

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Graph r = 4 sin r θ 0 0 sin
Graph r = 4 sin r θ 0 0 π /2 sin

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Graph r = 4 sin r θ 0 0 4 π /2 sin
Graph r = 4 sin r θ 0 0 4 π /2 π sin

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Graph r = 4 sin r θ 0 0 4 π /2 0 π sin
Graph r = 4 sin r θ 0 0 4 π /2 0 π 3 π /2 sin

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Graph r = 4 sin r θ 0 0 4 π /2 0 π -4 3 π /2 sin
Graph r = 4 sin r θ 0 0 4 π /2 0 π -4 3 π /2 2 π sin

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Graph r = 4 sin r θ 0 0 4 π /2 0 π -4 3 π /2 0 2 π sin
r = 2(1 - cos ) Cardiod r θ

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r = 2(1 - cos ) Cardiod r θ 0
r = 2(1 - cos ) Cardiod r θ 0 0

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r = 2(1 - cos ) Cardiod r θ 0 0 π /2
r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2

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r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 π
r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 4 π

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r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 4 π 3 π /2
r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 4 π 2 3 π /2

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r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 4 π 2 3 π /2 2 π
r = 2(1 - cos ) Cardiod r θ 0 0 2 π /2 4 π 2 3 π /2 0 2 π 4 2 2

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r θ r = 1 2 cos Limacon
r θ -1 0 r = 1 2 cos Limacon

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r θ -1 0 1 π /2 r = 1 2 cos Limacon
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This document was uploaded on 10/27/2011 for the course MATH 1352 at Texas Tech.

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Calculus2.2 - Section 6.3: Polar Forms & Area Polar...

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