Sketching Curves in Polar Coordinates Example 1.Sketch the curve r=0,0>0 in polar coordinates. Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Ine.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates Example 1. Sketch the curve r = θ, θ ≥ 0 in polar coordinates
[x] [x寻可 [居x詞 Polar axis [r,T] [2x,2z [x,] [服] [π，] r=00≤0≤2元 spiral of Archimedes Figure 10.3.1 Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Ine.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved
Sketching Curves in Polar Coordinates Example 2 Sketch the curve r=1-2 cos 0 in polar coordinates. y=cos0 27 Figure 10.3.2 Hille,Etgen Calculus One and Several Main Menu Copy right 2007 John Wiley Sors,Ine.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates Example 2 Sketch the curve r = 1 – 2 cos θ in polar coordinates. y = cos
Sketching Curves in Polar Coordinates [-10] 【-1,0j polar axis 3,T1 polar axis 0585 0≤8≤x 【-1,0j pofar axis polar axis 0s0s号x 0s8≤2m Figure 10.3.3 Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates
Sketching Curves in Polar Coordinates Example 3 Sketch the curve r=cos 20 in polar coordinates. 27 Figure 10.3.4 Sals,Hille,Etgen Calculus One and Several Varibles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates Example 3 Sketch the curve r = cos 2θ in polar coordinates
1 0≤0≤4π 050527 0s0six 0≤0≤π 0s0s5 050537 0s0six 0≤0≤2元 Figure 10.3.5 Salas,Hille,Etgen Calculus:One and Several Vartsbles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved
Example Sketch r=1+cos in polar coordinates Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Example Sketch r = 1 + cos θ in polar coordinates
Sketching Curves in Polar Coordinates Example 4 Rotating the curve r=1+cos by radians(measured in the counterclockwise direction),we obtain r=1+cos(0-π)=1+sin8. r=1+c0s8 r=1 +sin 8 rm 1-cos 8 ra 1-sin 6 Figure 10.3.6 Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Sketching Curves in Polar Coordinates 2 1 2 1 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Example 4 Rotating the curve r = 1 + cos θ by radians (measured in the counterclockwise direction) , we obtain 2 1
Sketching Curves in Polar Coordinates Lines:0=a,r=a sec 0,r=a csc 0. x=-2 yh y=2 0= 0=5 r=-2 sec 0 r=2 csc0 Figure 10.3.7 Salas,Hille,Etgen Calculus:One and Several Varisbles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates Lines : θ = a, r = a sec θ, r = a csc θ
Sketching Curves in Polar Coordinates Circles:r=a.r=a sin 0. r=a cos 0. r=2 r=-2 r=4 sin 0 r=-4c0s0 Figure 10.3.8 Sals,Hille,Etgen Calculus One and Several Varibles Main Menu Copy right 2007 John Wiley Sors,Inc.All rights reserved
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Sketching Curves in Polar Coordinates Circles : r = a, r = a sin θ, r = a cos θ