![Page 1: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/1.jpg)
March 14, 2012
6.5: Graphing Polar Equations
1. y = cosx 2. y = sinx
![Page 2: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/2.jpg)
March 14, 2012
r = cosθ
![Page 3: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/3.jpg)
March 14, 2012
r = sinθ
![Page 4: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/4.jpg)
March 14, 2012
y = 3cos θ
![Page 5: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/5.jpg)
March 14, 2012
Algebraic Relationship
r = cos O
![Page 6: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/6.jpg)
March 14, 2012
r = sin O
![Page 7: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/7.jpg)
March 14, 2012
![Page 8: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/8.jpg)
March 14, 2012
Symmetry:
1. line O =
2. polar axis
3. the pole
(r,θ)
(r,θ)
(r,θ)
![Page 9: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/9.jpg)
March 14, 2012
Use polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 sin 3θ
![Page 10: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/10.jpg)
March 14, 2012
Find the maximum r-value of the following graphs.
1. r = 3 + 2cos θ 2. r = 4 - sin θ
Maximum r-value: value occurring at a point the maximum distance from the pole.
*To find: find values of |r| as opposed to the directed distance r.
![Page 11: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/11.jpg)
March 14, 2012
Analyze the graph of the polar curve.
r = -3 cos 4θ
Domain:___________________Range:____________________Continuity:_________________Boundedness: ______________Symmetry: ________________Maximum r-value: ___________Asymptotes:_______________
![Page 12: 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r = a + b sin θ--Lemniscates: r 2 = a 2 sin 2θ r 2 = a 2 cos 2θ Spiral of Archimedes:](https://reader030.vdocuments.net/reader030/viewer/2022040122/5f0c80eb7e708231d435bb1e/html5/thumbnails/12.jpg)
March 14, 2012
Rose Curves: r = a cos nθr = a sin nθ
Limacon Curves: r = a + b cos θr = a + b sin θ
--
Lemniscates: r2 = a2sin 2θ
r2 = a2cos 2θ
Spiral of Archimedes: r = θ
where n is an integer > 1
n is even: 2n petalsn is odd: n petals
r-value max = a + b
where a > 0, b > 0