Explain the different types of polar graphs and their equations. Find sites with images of each. **Hint use google and search the images tab. Images can be pasted into blogger and include the link. You should have different sites.
I am hoping that polar coordinates is the same thing as polar graphs because that is all I can find. It sounds like the same thing to me though. Anyways, there are five types of polar graphs. 1. Cardiods 2. Lemniscates 3. Limacons 4. Spirals 5. Rose curves. ( All of these equations can be either cos or sin )
Cardiod – r = a +/- cos theta http://www.mathwords.com/c/cardioid.htm
Lemniscate – r^2 = a^2 cos 2 theta http://www.mathwords.com/l/lemniscate.htm
Limacon - r = b + a cos θ http://www.mathwords.com/l/limacon.htm
rose curve – a cos (some # ) theta http://www.mathwords.com/r/rose_curve.htm
spiral – r = a theta http://www.mathwords.com/s/spiral.htm
We learned about these different types of polar graphs in a chapter, and it was very simple. ( I think it was chapter 11? ) All we really had to do was tell which type of graph it was from the given equation, but we didn’t have to actually graph them.
Graphing a polar equation is accomplished pretty much the same way as rectangular equations are graphed. There are five types of polar equations.
1. Circles in Polar Form r=a sin theta or r=a cos theta The graph would be a circle on the horizontal(cos) axis or vertical (sin) axis.
2. Limacons (Snails) r=a ± b sin theta or r=a ± b cos theta where a > 0 and b > 0 The limacons containing sin will be above (+) or below (-) the horizontal axis. Limacons containing cos will be to the right (+) or to the left (-) of the vertical axis. The ratio of a/b will determine the exact shape.
3. Rose Curves r= a sin n theta or r=a cos n theta The number of petals that are present will depend on the value of n. If n is an even integer, then the rose will have 2n petals. If it is an odd integer, the rose will have n petals.
4. Lemniscates r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0
5. Cardiod r=a +/- cos theta or r=a +/- sin theta
We’ve already learned about these equations and graphs.. not sure what chapter it was though. This site includes the packet we received and images of the graphs.. http://www.alamo.edu/sac/slac/pdfs/math2412/grphpeqs.pdf
A while ago we learned polar graphs. The interesting things about polar graphs are their unique shape. There are six different types of polar graphs. Each graph has its own shape and equation. The different types of polar graps:
The Limacons, are also known as the snails. limacons may or may not have inner loops. 1.The formulas for limacons are: a ± b sin theta or a ± b cosine theta if a/b <1 then the limacon will have an inner loop. Ex. 2=3cos (60) is a limacon. Because a/b is greater than one this limacon has no inner loops.
2. Circles Circles have the most simple formula. Acosine theta or Asine theta where A can be any number including 1. http://jwilson.coe.uga.edu/EMAT6680Fa05/Alford/Assign11/image2.gif
3. The Rose Curve are very pretty and have petals(like flowers) The formulas are: r=a sin nθ OR r=a cos nθ *the number of petals are determined by n. If n is an even integer then the number of petals is = to 2(n) http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg
Leminscates- these graphs have a r^2 or the sqrt of r.
r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0 http://merganser.math.gvsu.edu/david/reed05/projects/kim/msri-jihokim/pics/lemniscate.png
the last is the Cardiod- the cardiod is like a heart. r = a +/- cosine theta http://www.walkingrandomly.com/images/mathematica/cardioid.gif
Polar graph is really unique with it shapes and there are six different types of polar graphs. Circles in polar form is r= a cos theta and r= a sin theta. Cos is represented as x and sin is represented as y. http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif Limacons(snails) - a ± b sin theta or a ± b cosine theta if a/b <1 then the limacon will have an inner loop. Example is 3+2cos theta.
Rose curves- r= a sin n theta or r=a cos n theta. If it is a even number it will have 2n but if it is odd it will just have n. http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg
Lemniscates- r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0. It can sometimes be like r=square root of 4 cos 2 theta. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations_files/image051.jpg
Graphing polar graphs are pretty easy. There are five different types of polar graphs.
1. Circles: r=a (sin)theta and r=a (cos)(theta) The graph would be a circle on either the horizontal or vertical axis.
2. Limacons: r=a +/- b sin theta or r=a +/- b cos theta where a > 0 and b > 0. The limacons containing sin will be above or below the horizontal axis, whereas Limacons containing cos will be to the right or to the left of the vertical axis.
3. Rose Curves:r=a sin n theta or r=a cos n theta.The number of petals will depend on the value of n. When you have an even number multiply by 2. If it is an odd number the rose will have have the number shown.
4. Lemniscates:r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a is not equal to 0
5. Cardiod:r=a +/- cos theta or r=a +/- sin theta
WEBSITES: http://www.seriesmathstudy.com/polargraph.htm This website contains all of the polar graphs listed above.
Lucky for me i actually have the packet of polar graphs..
You can graph a polar equation 5 different ways. It can be graphed by point-plotting, using the trigonometric functions period, and using the equation's symmetry (if any).
1.CIRCLES IN POLAR FORM *Circle equation has no (+)(-)
There are many types of polar graphs. We actually learned a few in class. TYPES: circles limacons (snails) cardoid rose lemniscates
The ones above we learned in class from the handout you gave us.
It's very easy to identify polar equations. IDENTIFYING:
1) r=4cos theta whatever the number is before the cos is considered a. a can be any number and when you see it like this its a CIRCLE.
2) r=8sin theta again, whatever the number is before sin is considered a. since this is a SIN problem its no different. it will still be a CIRCLE.
3) 4+/-7sin theta whenever you see a plus or minus its a LIMACON(snail) in a graph if you see a LOOP it is also another sign of a limacon.
4) 6+/-6sin theta *although this seems exactly like a limacon its not! this is a CARDOID. ***the difference is with a limacon you will have a/b greater, lesser, or equal to. so in example 3 it would be 4/7.
5) r=5sin 8 theta THESE ARE MY FAVORITE! this is called a ROSE curve. since the number in front of theta (which is n) is even then you multiply 2x8 to get the number of petals in your graph. if its an odd number then you just keep the number the same and that's your amount of petals.
6) r^2=2^2sin 2 theta when you have something squared it's automatically a LEMNISCATE.
Here are all the types of Polar graphs and their equations: There are five different polar graphs Circles r = a cos theta r = a sin theta http://media.texample.net/tikz/examples/PNG/polar-coordinates-template.png Limacons aka Snails r = a plus or minus b sin theta a > 0 and b > 0 r = a plus or minus b cos theta a > 0 and b > 0 A and b are both numbers http://curvebank.calstatela.edu/index/limacon.gif Cardiod r = a plus or minus a sin theta r = a plus or minus a cos theta The numbers are always the same http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png Rose Curves r = a sin ntheta r = a cos ntheta There is a number in front of theta To determine the petals if it is even you multiply the number by 2 and if it is odd then it is the same number http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg Lemniscates R2 = a2 sin 2 theta R2 = a2 cos 2 theta The number is squared http://curvebank.calstatela.edu/index/lemniscate.gif
The different types of Polar graphs and there equations are:
1)Circles: r=acos(theta), r=asin(theta) ; In this a can be any number.
2) Limacons: r= a +/- b sin(theta), r= a +/- b sin(theta). If a/b turns out to be less than one in this type of problem then there are inner loops.
3)Cardiods: r= a +/- a sin(theta), r= a +/- a cos(theta). In this equation the same number is repeated twice. The shape comes out looking like a distorted heart.
4) Rose Curves: r= a sin n(theta), r= acos n(theta). In rose curves if n is an even integer, then the rose will have 2n petals.
5)Lemniscates: r^2 = a^2 sin 2(theta), r^2= a^2 cos 2(theta) where is not equal to 0.
Rose Curves, Circles, and Cardiods-http://www.mathamazement.com/Lessons/Pre-Calculus/06_Additional-Topics-in-Trigonometry/graphs-of-polar-equations.html
There are 5 different types of polar graphs which are, circles, lemniscates, rose curves, cardiods, and limacons. They all have different formulas that you can determine which one is which.
The first one is circles. The formula for a circle is R = acos (theta) and R = asin (theta). a = a number. http://www.tutorvista.com/topic/graphs-of-polar-equations
The next is lemniscates. The formula for lemniscate is R^2 = a^2 sin 2 (theta), R^ 2 = a^ 2 cos 2 (theta). A can equal anything except zero. http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations.htm
Next is rose curves. It’s formula is R = a sin n(theta) and R= acos n(theta). If n is an odd number, then it will have that many petals. If it is an even number then it will have double. http://radiantbytes.com/books/python-latex/src/chap5.html
Cardiods. The formula for this is R = a + or - a sin (theta) and R = a +or- a cos (theta). the a’s are the same. http://www.walkingrandomly.com/?p=67
Last is Limacons. The formula is R = a +/- b sin (theta), R = a +/- b sin (theta). if a over b is less than one then it will have inner loops. http://www.mathhelpforum.com/math-help/f6/limacon-area-52948.html
I am hoping that polar coordinates is the same thing as polar graphs because that is all I can find. It sounds like the same thing to me though. Anyways, there are five types of polar graphs. 1. Cardiods 2. Lemniscates 3. Limacons 4. Spirals 5. Rose curves.
ReplyDelete( All of these equations can be either cos or sin )
Cardiod – r = a +/- cos theta
http://www.mathwords.com/c/cardioid.htm
Lemniscate – r^2 = a^2 cos 2 theta
http://www.mathwords.com/l/lemniscate.htm
Limacon - r = b + a cos θ
http://www.mathwords.com/l/limacon.htm
rose curve – a cos (some # ) theta
http://www.mathwords.com/r/rose_curve.htm
spiral – r = a theta
http://www.mathwords.com/s/spiral.htm
We learned about these different types of polar graphs in a chapter, and it was very simple. ( I think it was chapter 11? ) All we really had to do was tell which type of graph it was from the given equation, but we didn’t have to actually graph them.
This comment has been removed by the author.
ReplyDeleteGraphing a polar equation is accomplished pretty much the same way as rectangular equations are graphed. There are five types of polar equations.
ReplyDelete1. Circles in Polar Form
r=a sin theta or r=a cos theta
The graph would be a circle on the horizontal(cos) axis or vertical (sin) axis.
2. Limacons (Snails)
r=a ± b sin theta or r=a ± b cos theta where a > 0 and b > 0
The limacons containing sin will be above (+) or below (-) the horizontal axis. Limacons containing cos will be to the right (+) or to the left (-) of the vertical axis. The ratio of a/b will determine the exact shape.
3. Rose Curves
r= a sin n theta or r=a cos n theta
The number of petals that are present will depend on the value of n. If n is an even integer, then the rose will have 2n petals. If it is an odd integer, the rose will have n petals.
4. Lemniscates
r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0
5. Cardiod
r=a +/- cos theta or r=a +/- sin theta
We’ve already learned about these equations and graphs.. not sure what chapter it was though.
This site includes the packet we received and images of the graphs..
http://www.alamo.edu/sac/slac/pdfs/math2412/grphpeqs.pdf
A while ago we learned polar graphs. The interesting things about polar graphs are their unique shape. There are six different types of polar graphs. Each graph has its own shape and equation. The different types of polar graps:
ReplyDeleteThe Limacons, are also known as the snails. limacons may or may not have inner loops.
1.The formulas for limacons are:
a ± b sin theta or
a ± b cosine theta
if a/b <1 then the limacon will have an inner loop.
Ex. 2=3cos (60) is a limacon. Because a/b is greater than one this limacon has no inner loops.
http://web.me.com/paulscott.info/DC/limacon/Limacon-graph.gif
2.
Circles
Circles have the most simple formula.
Acosine theta or Asine theta where A can be any number including 1.
http://jwilson.coe.uga.edu/EMAT6680Fa05/Alford/Assign11/image2.gif
3. The Rose Curve are very pretty and have petals(like flowers)
The formulas are:
r=a sin nθ OR r=a cos nθ
*the number of petals are determined by n. If n is an even integer then the number of petals is = to 2(n)
http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg
Leminscates- these graphs have a r^2 or the sqrt of r.
r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0
http://merganser.math.gvsu.edu/david/reed05/projects/kim/msri-jihokim/pics/lemniscate.png
the last is the Cardiod- the cardiod is like a heart. r = a +/- cosine theta
http://www.walkingrandomly.com/images/mathematica/cardioid.gif
Polar graph is really unique with it shapes and there are six different types of polar graphs.
ReplyDeleteCircles in polar form is r= a cos theta and r= a sin theta. Cos is represented as x and sin is represented as y.
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
Limacons(snails) - a ± b sin theta or a ± b cosine theta
if a/b <1 then the limacon will have an inner loop. Example is 3+2cos theta.
http://wps.prenhall.com/wps/media/objects/682/698936/Chapter06/6m6_4q1d.gif
Cardiod - r=a +/- cos theta or r=a +/- sin theta. Example is 2+/- 2 sin theta.
http://www.math.wvu.edu/~mays/AVdemo/Labs/serve_new_quiz_show_files/opcpolar.jpg
Rose curves- r= a sin n theta or r=a cos n theta. If it is a even number it will have 2n but if it is odd it will just have n.
http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg
Lemniscates- r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a ≠ 0. It can sometimes be like r=square root of 4 cos 2 theta.
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations_files/image051.jpg
Graphing polar graphs are pretty easy. There are five different types of polar graphs.
ReplyDelete1. Circles: r=a (sin)theta and r=a (cos)(theta)
The graph would be a circle on either the horizontal or vertical axis.
2. Limacons: r=a +/- b sin theta or r=a +/- b cos theta where a > 0 and b > 0. The limacons containing sin will be above or below the horizontal axis, whereas Limacons containing cos will be to the right or to the left of the vertical axis.
3. Rose Curves:r=a sin n theta or r=a cos n theta.The number of petals will depend on the value of n. When you have an even number multiply by 2. If it is an odd number the rose will have have the number shown.
4. Lemniscates:r^2 = a^2 sin 2 theta or r^2= a^2 cos 2 theta, where a is not equal to 0
5. Cardiod:r=a +/- cos theta or r=a +/- sin theta
WEBSITES:
http://www.seriesmathstudy.com/polargraph.htm
This website contains all of the polar graphs listed above.
Thanks.
Lucky for me i actually have the packet of polar graphs..
ReplyDeleteYou can graph a polar equation 5 different ways. It can be graphed by point-plotting, using the trigonometric functions period, and using the equation's symmetry (if any).
1.CIRCLES IN POLAR FORM
*Circle equation has no (+)(-)
r=acosθ
r=asinθ
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
2.LIMACONS (SNAILS)
*a & b are numbers
r=a +/- bsinθ, where a>0 and b>0
r=a +/- bcosθ, where a>0 and b>0
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image008.gif
3.CARDIOD
*Same numbers
r= a +/- asinθ
r= a +/- acosθ
http://www.centipedia.com/images/en/6/63/CardioidsLabeled.PNG
4.ROSE CURVES
*Number infront of θ
r= asin nθ
r= acos nθ
-If n is an even integer, then the rose will have 2n petals.
-If n is an odd integer, then t he rose will have n petals.
http://www.dreamcalc.com/dchelp/fxgraph_polar.gif
5.LEMNISCATES
*squared or 2 infront of θ
r^2=a^2 sin 2θ
r^2=a^2 cos 2θ
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image034.jpg
There are many types of polar graphs. We actually learned a few in class.
ReplyDeleteTYPES:
circles
limacons (snails)
cardoid
rose
lemniscates
The ones above we learned in class from the handout you gave us.
It's very easy to identify polar equations.
IDENTIFYING:
1) r=4cos theta
whatever the number is before the cos is considered a.
a can be any number and when you see it like this its a CIRCLE.
2) r=8sin theta
again, whatever the number is before sin is considered a.
since this is a SIN problem its no different. it will still be a CIRCLE.
3) 4+/-7sin theta
whenever you see a plus or minus its a LIMACON(snail)
in a graph if you see a LOOP it is also another sign of a limacon.
4) 6+/-6sin theta
*although this seems exactly like a limacon its not!
this is a CARDOID.
***the difference is with a limacon you will have a/b greater, lesser, or equal to.
so in example 3 it would be 4/7.
5) r=5sin 8 theta
THESE ARE MY FAVORITE!
this is called a ROSE curve.
since the number in front of theta (which is n) is even then you multiply 2x8 to get the number of petals in your graph.
if its an odd number then you just keep the number the same and that's your amount of petals.
6) r^2=2^2sin 2 theta
when you have something squared it's automatically a LEMNISCATE.
Here are all the types of Polar graphs and their equations:
ReplyDeleteThere are five different polar graphs
Circles
r = a cos theta
r = a sin theta
http://media.texample.net/tikz/examples/PNG/polar-coordinates-template.png
Limacons aka Snails
r = a plus or minus b sin theta a > 0 and b > 0
r = a plus or minus b cos theta a > 0 and b > 0
A and b are both numbers
http://curvebank.calstatela.edu/index/limacon.gif
Cardiod
r = a plus or minus a sin theta
r = a plus or minus a cos theta
The numbers are always the same
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png
Rose Curves
r = a sin ntheta
r = a cos ntheta
There is a number in front of theta
To determine the petals if it is even you multiply the number by 2 and if it is odd then it is the
same number
http://jwilson.coe.uga.edu/EMAT6680Fa08/Ruff/Ruff%20assignment%2011/complgraph.jpg
Lemniscates
R2 = a2 sin 2 theta
R2 = a2 cos 2 theta
The number is squared
http://curvebank.calstatela.edu/index/lemniscate.gif
The different types of Polar graphs and there equations are:
ReplyDelete1)Circles: r=acos(theta), r=asin(theta) ; In this a can be any number.
2) Limacons: r= a +/- b sin(theta), r= a +/- b sin(theta). If a/b turns out to be less than one in this type of problem then there are inner loops.
3)Cardiods: r= a +/- a sin(theta), r= a +/- a cos(theta). In this equation the same number is repeated twice. The shape comes out looking like a distorted heart.
4) Rose Curves: r= a sin n(theta), r= acos n(theta). In rose curves if n is an even integer, then the rose will have 2n petals.
5)Lemniscates: r^2 = a^2 sin 2(theta), r^2= a^2 cos 2(theta) where is not equal to 0.
Rose Curves, Circles, and Cardiods-http://www.mathamazement.com/Lessons/Pre-Calculus/06_Additional-Topics-in-Trigonometry/graphs-of-polar-equations.html
Limacons-http://web.me.com/paulscott.info/DC/limacon/limacon-expl.html
Lemniscates-http://www.composedwithcomposites.org/about_logo.html
There are 5 different types of polar graphs which are, circles, lemniscates, rose curves, cardiods, and limacons.
ReplyDeleteThey all have different formulas that you can determine which one is which.
The first one is circles. The formula for a circle is R = acos (theta) and R = asin (theta). a = a number.
http://www.tutorvista.com/topic/graphs-of-polar-equations
The next is lemniscates. The formula for lemniscate is R^2 = a^2 sin 2 (theta), R^ 2 = a^ 2 cos 2 (theta). A can equal anything except zero.
http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations.htm
Next is rose curves. It’s formula is R = a sin n(theta) and R= acos n(theta). If n is an odd number, then it will have that many petals. If it is an even number then it will have double.
http://radiantbytes.com/books/python-latex/src/chap5.html
Cardiods. The formula for this is R = a + or - a sin (theta) and R = a +or- a cos (theta). the a’s are the same.
http://www.walkingrandomly.com/?p=67
Last is Limacons. The formula is R = a +/- b sin (theta), R = a +/- b sin (theta). if a over b is less than one then it will have inner loops.
http://www.mathhelpforum.com/math-help/f6/limacon-area-52948.html