What are the different types of polar graphs? Give several examples with pictures or a site to use as a reference. Everyone should have different pictures or a different site.
Polar Graphs There are six types of polar graphs – circles, cardioids, lemniscates, limacons, rose curves, and spirals.
Circles: Equation– r = a cos theta & r = a sin theta (“a” is the diameter of the circle that has its left-most/ bottom-most edge at the pole). Its shape is a simple circle.
Limacon (Snails): Equation – r = a +/- b sin theta, where a>0 and b>0 & r = a +/- cos theta, where a<0 and b<0. The ratio of a/b will determine the exact shape of the limacon. Its shape is a circle with an inner loop.
Cardioid: A cardioids is a type of limacon. If a = b, it is a cardioid. A cardioid is a curve that is somewhat heart shaped. Equation – r = a+/- a cos theta & r = a +/- a sin theta
Rose Curve: A smooth curve with leaves arranged symmetrically about a common center. The examples below all have polar equations using cosine, but sin may be used too. Formula – r = a sin ntheta and r = a cos ntheta *If n is an even integer, then the rose will have 2n petals, but if n is an odd integer, then the rose will have n petals.
Spiral: A curve on a plane that turns endlessly outward of inward (or even both).
Lemniscates: Has the shape of a figure-8 or propeller. Equation – r^2= a^2 sin 2theta and r^2= a^2 cos 2theta
Polar equations are commonly graphed with polar coordinates but can also be graphed with point-plotting, using the trig functions period, and using the equation’s symmetry (if any). Wellllll I did have all kind of pictures with each type, but for some reason they aren't showing up? They are all on our handout from class though, minus the spiral. http://www.mathwords.com/p/polar_curves.htm
POLAR GRAPHS: (circles, limacons, cardiods, rose curves, lemniscates) -can be graphed by point-plotting, using the trigonometric functions period, and using the equation's symmetry
1. Cirlces r=acosθ where "a" is the diamter of the cirlce that has its left-most edge at the pole.
r=asinθ where "a" is the dimater of the circle that has its bottom-most edge at the pole.
2.Limacons (Snails) r=a +/- bsinθ where a>0 and b>0 r=a +/- bcosθ where a>0 and b>0 *The ratio of a/b will determine the exact shape of the limacon
The limacos containging sine wil be above the horizontal axis if the sign between a and b is plus or beloew the horizontal axis if the sign is minus. If the limacon contains the function cosine then the graaph will be either to the right of the vertical axis if the sign is plus or to the left if the sign is minus.
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image024.jpg (with an inner loop)
3.Cardioid r=a+/-asinθ r=a+/-cosθ *Same numbers as "a"
4.Rose Curves r=a sin nθ OR r=a cos nθ, *If n is an even integer, then the rose will have 2n petals. If n is an odd integer, then the rose will have n petals.
The number of petals present will depend on the value of n. The value of "a" will determine the length.
5.Lemniscates r^2=a^2 sin 2θ or r^2=a^2 cos 2θ *r^2 also can be represented as a squared root
A lemniscate containing the sine function will be symmetric to the pole while the lemnsicate containing the cosine function will be summetric to the polar axis, to θ=pi/2 and the pole.
We recieved a packet this week that had six different polar graphs in it: Circles, Limacons, Cardioids, Rose Curves, Lemnisicates, and Spirals
Circles r = a cos theta r = a sin theta (a is the diameter of a circle that has a left most/bottom most edge at the pole)
Cardioids: r = a +/- a cos theta r = a +/- a sin theta
Limacons (Snails): r = a +/- b sin theta where a > 0 and b > 0 r = a +/- b cos theta where a < 0 and b > 0
Rose Curves: r = a sin ntheta r = a cos ntheta
Lemnisicates: r2 = a2 sin 2theta r2 = a2 cos 2theta
Spiral: A curve on out.the plane that will turn in or out.
Okay so I am super mad because I have pictures of all of the graphs but the blog will not let me post them. It tells me my HTML cannot be accepted: Must be at most 4,096 characters. I don't know what that means sooooo yeah...I'm mad! Sorryyyy :/
This week we learned a little about polar graphs which will be on our tests and quizzes throughout section 11. There are six different types of graphs: circle, cardiods, limacons, lemniscates, spirals, and rose curves.
This website will give you a picture of all of the graphs if you click on the link to the name of the polar graph you want to look at: http://www.mathwords.com/p/polar_curves.htm
They have all examples except for circle, but that one is pretty self explanatory. It looks just like a circle. The equation for it is r= a cos theta. “a” can be any number.
Cardiods: R= a +/- a sin theta or r = a +/- a cos theta The “a’s” in the problem have to be the same number
Limacons: R= a +/- b sin theta where a > 0 and b > 0 or r = a +/- b cos theta where a > 0 and b >0 The “a and b” have to be different numbers.
Rose curves: R = a sin ntheta or r = a cos ntheta This graph will have an “n” before the theta. The number of loops depends on this number. If it is even, the number of loops is doubled, if it is odd, the number remains the same.
Lemniscates: R^2 = a ^2 sin 2theta or r^2 = a ^2 cos 2theta You can tell these because the “r” is squared and there is a 2 in front of the theta.
In order to create Radar graphs the module "jpgraph_polar.php" must first be included.
Each data point in a polar plot is represented by a tuple consisting of a radius and an angle. The polar plot itself can be either outlined or filled. In addition each point may have a standard marker (the same as for line and scatter plots).
The scale for the radius can be either linear or logarithmic.
A polar graph is created by creating an instance of class PolarGraph. The polar graph type inherits all the capabilities of ordinary x,y graphs, i.e they can have background images, background gradients, formatted titles, using tabbed titles etc.
There are two types of polar graphs, full 360 degree view or just 180 degree view. The figures below show the difference between these two graph types.
Figure 16.42. A full 360 degree polar graph (polarex0.php)
Figure 16.43. A 180 degree (half) polar graph (polarex0-180.php)
There are many types of polar graphs. We actually learned a few the other day in class. TYPES: circles limacons (snails) cardoid rose lemniscates
The ones above we learned in class from the handout you gave us. I'm having a lot of trouble being able to open anything when i google diferent types of polar equations so i'm just getting all my information from that handout.
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.
The six types of polar graphs are: circles, cardioids, lemniscates, limacons, rose curves, and spirals.
Circles: Equation is r =(a)cos(theta)and r = (a) sin(theta)a is the diameter of the circle. The shape is obivously a circle!
Limacon (Snails):Equation is r = a+/-bsintheta, where a>0 and b>0 and r = a+/-costheta, where a<0 and b<0.The shape is a circle with a inner loop.
Cardioid:Equation is r = a+/-acostheta and r=a+/-asintheta. A cardioids is just another type of limacon. If a=b, it is a cardioid. A cardioid is a shape that is kind of like a heart.
Rose Curve: Formula is r=asinntheta and r=acosntheta. A rose curve is a smooth curve with leaves arranged symmetrically about a common center.
*If n is an even integer, then the rose will have 2n petals, but if n is an odd integer, then the rose will have n petals.
Lemniscates:Equation is r^2= a^2sin2theta and r^2=a^2cos2theta. The shape is an 8.
Polar graphs. This week we started learning about polar graphs and what shapes they make in chapter eleven. There are five types of polar graphs. They are circles, limacons (or snails), cardoid, rose curves, and lemniscates.
Circles can be determined by what type of things are in its equation. Its equation is r = a cos theta. If there is anything else in the equation it is not a circle.
http://en.wikipedia.org/wiki/Circle_graph
Limacons (or snails) can be determined by what is in their equation also. It has two equations. They are: r = a +or- b sin theta. (a and b are greater than zero) and r = a +or- b cos theta. (a and b are greater than zero)
Rose curves depend on their equation too. The equation is r = a sin ntheta or r = a cos ntheta. If n is an even number, the rose will have double the petals. If it is an odd number it will have that amount of petals on the graph.
http://www.dreamcalc.com/dchelp/fxgraph_polar.gif
Lemniscates have two equations. They are: r^2 = a^2 sin 2 theta, and r^2 = a^2 cos 2 theta, where a doesn’t equal zero.
This week we learned about polar and how to graph them. There are six types of polar graphs. Types of Polar graphs: -Circle -Limacons (snails) -Cardioid -Rose Curves -Lemniscates Circles: There are two equations while dealing polar circles. The equations are r= a cos theta & r= a sine theta. (“a” is the diameter of the circle that has its left-most edge/bottom-most edge at the pole). This polar graph simply makes a shape of a circle. http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
Limacons (snails) There are two equations. But this one has a +/-, a and b. Equations are r=a +/- b sin theta, where a>0 and b>0. Next one is r= a +/- b cos theta, where a>0 and b>0. http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image024.jpg
Cardioid: There are two equations. The number front of the plus and the the cos/sin are the same which is A. Equations are r= a+/-a sin theta, r= a+/- a cos theta. Example is like 2 +/- 2 sin theta = cardioid. http://www.faculty.umassd.edu/adam.hausknecht/temath/TEMATH2/Examples/Assets/PolarTaylorPolynomials/Cardioid_stopped.gif
Rose Curves. Graph that is produced from a polar equation in the form of : r=a sin ntheta or r=a cos ntheta, where a doesn’t equal to 0 and n is an integer>1. if n is a even integer, then the rose will have 2n petals if it is odd it will have n petals. http://us.monografias.com/docs33/polar-coordinate/Image5617.gif
Lemniscates: Containing the sine function will be symmetric to the pole while the lemiscate containing the cosine function will be symmetric to the polar axis, to theta= pi/2, and the pole. Equations are r squared= a squared sin 2theta or r squared= a squared cos 2theta, where a doesn’t equal to 0. http://jwilson.coe.uga.edu/EMAT6680Su06/Swanagan/Assignment1/Asmt1prob10dpic3.gif Spiral:
It a curve on the plane that never end which basically makes endlessly outward or inward sometimes it can do both. http://www.mathamazement.com/images/Pre-Calculus/06_Additional-Topics-in-Trigonometry/06_04_graphs-of-polar-equations/logarithmic-spiral.jpg
This week we discussed polar and rectangular. We also learned polar graphs. The interesting thing about polar graphs is the unique shape they make. There are six different types of polar graphs. Each graph has its own shape and equation. The different types of polar graphs are as follows: 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. http://digilander.libero.it/roberto20129/matematica/img_curve/Limacon1.gif”>Limacon graph 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( my favorite) are the prettiest. 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”>Rose Petal Graph
4.The Cardiods The cardiods are related to the limacons. A and b must be equal , or A+Asin theta or B-Bsine theta http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png”>Cardiod Graph
5. The Lemniscates r^2=a^2 sin 2θ or r^2=a^2 cos 2θ “r^2” may also be represented as r=sqrt http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations_files/image065.jpg”>Leminscates graph 6. The last are spirals : Spirals are curves on planes that will turn in or out. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image006.jpg”>Spiral Graph
We were introduced to polar graphs this week in Chapter 11. We will be tested and quized on these types of graphs and need to be able to recognize them. There are six different types of graphs: circle, cardiods, limacons, lemniscates, spirals, and rose curves.
This website: http://www.mathwords.com/p/polar_curves.htm will give you illustrations of the graphs by simply clicking the name of the polar graph you want to see.
The only polar graph they do not have an illustration to is the circle, but you can find a picture of the circle graph in the handout we got on Monday. It looks just like a circle. The equation for it is r= a cos theta. “a” can be any number. Be careful when there is no number infront of the cos or sin it could be understood as 1.
Cardiods: R= a +/- a sin theta or r = a +/- a cos theta The “a’s” in the problem have to be the same number
Limacons: R= a +/- b sin theta where a > 0 and b > 0 or r = a +/- b cos theta where a > 0 and b >0 The “a and b” have to be different numbers.
Rose curves: R = a sin ntheta or r = a cos ntheta This graph will have an “n” before the theta. The number of loops depends on this number. If it is even, the number of loops is doubled, if it is odd, the number remains the same.
Lemniscates: R^2 = a ^2 sin 2theta or r^2 = a ^2 cos 2theta You can tell these because the “r” is squared and there is a 2 in front of the theta.
This week in advanced math we got a packed that showed us the polar graphs and there formulas. Here are the different types of graphs we learned.
Circles in Polar form: I learned the hard way that this is the name of this type of graph and not just a polar graph. When graphed this type of polar equation looks like a circle. The formula for this type of polar equation is r=a cos(theta) where "a" is the diameter of the circle that has its left most edge at the pole. The other formula is r=a sin(theta) where "a" is the diameter of the circle that has its bottom-most edge at the pole.
Limacons(Snails): The formulas for Limacons are r=a+/- b sin(theta), where a>0 and b>0. and r=a+/- b cos(theta), where a>0 and b>0. If your answer is less than 1 you will have an inner loop.
Cardiods: Based on the name you can tell that they are sort of a heart shape, but a distorted heart. Cardiods are like Limacons but they occur when you have the same number twice, like two a's instead of an a and a b. The formula is r=a+/- a sin(theta) and r=a +/- acos(theta)
Rose Curves: Rose Curves occur when n is times theta. r= a sin n(theta) or r=a cos n(theta), where a is not equal to 0 and n is an integer > 1. They are called rose curves because they form loops that resemble petals.
Lemniscates: Involves numbers being squared. r^2= a^2 sin 2(theta) or r^2= a^2 cos 2(theta), where a is not equal to 0.
You can find these pictures at http://www.mathamazement.com/Lessons/Pre-Calculus/06_Additional-Topics-in-Trigonometry/graphs-of-polar-equations.html or
Polar Graphs
ReplyDeleteThere are six types of polar graphs – circles, cardioids, lemniscates, limacons, rose curves, and spirals.
Circles:
Equation– r = a cos theta & r = a sin theta (“a” is the diameter of the circle that has its left-most/ bottom-most edge at the pole). Its shape is a simple circle.
Limacon (Snails):
Equation – r = a +/- b sin theta, where a>0 and b>0 & r = a +/- cos theta, where a<0 and b<0. The ratio of a/b will determine the exact shape of the limacon. Its shape is a circle with an inner loop.
Cardioid:
A cardioids is a type of limacon. If a = b, it is a cardioid. A cardioid is a curve that is somewhat heart shaped. Equation – r = a+/- a cos theta & r = a +/- a sin theta
Rose Curve:
A smooth curve with leaves arranged symmetrically about a common center. The examples below all have polar equations using cosine, but sin may be used too. Formula – r = a sin ntheta and r = a cos ntheta
*If n is an even integer, then the rose will have 2n petals, but if n is an odd integer, then the rose will have n petals.
Spiral:
A curve on a plane that turns endlessly outward of inward (or even both).
Lemniscates:
Has the shape of a figure-8 or propeller. Equation – r^2= a^2 sin 2theta and r^2= a^2 cos 2theta
Polar equations are commonly graphed with polar coordinates but can also be graphed with point-plotting, using the trig functions period, and using the equation’s symmetry (if any). Wellllll I did have all kind of pictures with each type, but for some reason they aren't showing up? They are all on our handout from class though, minus the spiral.
http://www.mathwords.com/p/polar_curves.htm
POLAR GRAPHS: (circles, limacons, cardiods, rose curves, lemniscates)
ReplyDelete-can be graphed by point-plotting, using the trigonometric functions period, and using the equation's symmetry
1. Cirlces
r=acosθ where "a" is the diamter of the cirlce that has its left-most edge at the pole.
r=asinθ where "a" is the dimater of the circle that has its bottom-most edge at the pole.
http://jwilson.coe.uga.edu/EMAT6680Fa06/Crumley/writeup11/Polar_files/image022.jpg
2.Limacons (Snails)
r=a +/- bsinθ where a>0 and b>0
r=a +/- bcosθ where a>0 and b>0
*The ratio of a/b will determine the exact shape of the limacon
The limacos containging sine wil be above the horizontal axis if the sign between a and b is plus or beloew the horizontal axis if the sign is minus. If the limacon contains the function cosine then the graaph will be either to the right of the vertical axis if the sign is plus or to the left if the sign is minus.
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image024.jpg (with an inner loop)
3.Cardioid
r=a+/-asinθ
r=a+/-cosθ
*Same numbers as "a"
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png
4.Rose Curves
r=a sin nθ OR r=a cos nθ,
*If n is an even integer, then the rose will have 2n petals. If n is an odd integer, then the rose will have n petals.
The number of petals present will depend on the value of n. The value of "a" will determine the length.
http://www.math.rutgers.edu/~greenfie/mill_courses/math152/gifstuff/polar_cosine_rose.gif
5.Lemniscates
r^2=a^2 sin 2θ or r^2=a^2 cos 2θ
*r^2 also can be represented as a squared root
A lemniscate containing the sine function will be symmetric to the pole while the lemnsicate containing the cosine function will be summetric to the polar axis, to θ=pi/2 and the pole.
http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations_files/image061.jpg
We recieved a packet this week that had six different polar graphs in it:
ReplyDeleteCircles, Limacons, Cardioids, Rose Curves, Lemnisicates, and Spirals
Circles
r = a cos theta
r = a sin theta
(a is the diameter of a circle that has a left most/bottom most edge at the pole)
Cardioids:
r = a +/- a cos theta
r = a +/- a sin theta
Limacons (Snails):
r = a +/- b sin theta where a > 0 and b > 0
r = a +/- b cos theta where a < 0 and b > 0
Rose Curves:
r = a sin ntheta
r = a cos ntheta
Lemnisicates:
r2 = a2 sin 2theta
r2 = a2 cos 2theta
Spiral:
A curve on out.the plane that will turn in or out.
Okay so I am super mad because I have pictures of all of the graphs but the blog will not let me post them. It tells me my HTML cannot be accepted: Must be at most 4,096 characters. I don't know what that means sooooo yeah...I'm mad! Sorryyyy :/
http://www.math.wpi.edu/Course_Materials/MA1023A03/polar/node1.html
This week we learned a little about polar graphs which will be on our tests and quizzes throughout section 11. There are six different types of graphs: circle, cardiods, limacons, lemniscates, spirals, and rose curves.
ReplyDeleteThis website will give you a picture of all of the graphs if you click on the link to the name of the polar graph you want to look at:
http://www.mathwords.com/p/polar_curves.htm
They have all examples except for circle, but that one is pretty self explanatory. It looks just like a circle. The equation for it is r= a cos theta. “a” can be any number.
Cardiods:
R= a +/- a sin theta or r = a +/- a cos theta The “a’s” in the problem have to be the same number
Limacons:
R= a +/- b sin theta where a > 0 and b > 0 or r = a +/- b cos theta where a > 0 and b >0 The “a and b” have to be different numbers.
Rose curves:
R = a sin ntheta or r = a cos ntheta This graph will have an “n” before the theta. The number of loops depends on this number. If it is even, the number of loops is doubled, if it is odd, the number remains the same.
Lemniscates:
R^2 = a ^2 sin 2theta or r^2 = a ^2 cos 2theta You can tell these because the “r” is squared and there is a 2 in front of the theta.
Polar graphs
ReplyDeleteIn order to create Radar graphs the module "jpgraph_polar.php" must first be included.
Each data point in a polar plot is represented by a tuple consisting of a radius and an angle. The polar plot itself can be either outlined or filled. In addition each point may have a standard marker (the same as for line and scatter plots).
The scale for the radius can be either linear or logarithmic.
A polar graph is created by creating an instance of class PolarGraph. The polar graph type inherits all the capabilities of ordinary x,y graphs, i.e they can have background images, background gradients, formatted titles, using tabbed titles etc.
There are two types of polar graphs, full 360 degree view or just 180 degree view. The figures below show the difference between these two graph types.
Figure 16.42. A full 360 degree polar graph (polarex0.php)
Figure 16.43. A 180 degree (half) polar graph (polarex0-180.php)
The choice is controlled with the method
PolarGraph::SetType($aType)
$aType is specified with the symbolic defines
POLAR_360, The default
POLAR_180
http://jpgraph.net/download/manuals/chunkhtml/ch16s03.html <= look there for correct pictures n_n
ReplyDeleteThere are many types of polar graphs. We actually learned a few the other day in class.
ReplyDeleteTYPES:
circles
limacons (snails)
cardoid
rose
lemniscates
The ones above we learned in class from the handout you gave us.
I'm having a lot of trouble being able to open anything when i google diferent types of polar equations so i'm just getting all my information from that handout.
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.
The six types of polar graphs are: circles, cardioids, lemniscates, limacons, rose curves, and spirals.
ReplyDeleteCircles: Equation is r =(a)cos(theta)and r = (a) sin(theta)a is the diameter of the circle. The shape is obivously a circle!
Limacon (Snails):Equation is r = a+/-bsintheta, where a>0 and b>0 and r = a+/-costheta, where a<0 and b<0.The shape is a circle with a inner loop.
Cardioid:Equation is r = a+/-acostheta and r=a+/-asintheta. A cardioids is just another type of limacon. If a=b, it is a cardioid. A cardioid is a shape that is kind of like a heart.
Rose Curve: Formula is r=asinntheta and r=acosntheta. A rose curve is a smooth curve with leaves arranged symmetrically about a common center.
*If n is an even integer, then the rose will have 2n petals, but if n is an odd integer, then the rose will have n petals.
Lemniscates:Equation is r^2= a^2sin2theta and r^2=a^2cos2theta. The shape is an 8.
Spiral: A curve on a plane that turns endlessly.
http://www.analyzemath.com/polarcoordinates/polarcoordinates.html
Polar graphs.
ReplyDeleteThis week we started learning about polar graphs and what shapes they make in chapter eleven. There are five types of polar graphs. They are circles, limacons (or snails), cardoid, rose curves, and lemniscates.
Circles can be determined by what type of things are in its equation. Its equation is r = a cos theta. If there is anything else in the equation it is not a circle.
http://en.wikipedia.org/wiki/Circle_graph
Limacons (or snails) can be determined by what is in their equation also. It has two equations. They are: r = a +or- b sin theta. (a and b are greater than zero) and r = a +or- b cos theta. (a and b are greater than zero)
http://upload.wikimedia.org/wikipedia/commons/7/72/Limacon_of_Pascal.png
Cardoid can also be determined by what is in its equation. Its equations are r = a +or- a sin theta, and r = a +or- a cos theta.
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png
Rose curves depend on their equation too. The equation is r = a sin ntheta or r = a cos ntheta. If n is an even number, the rose will have double the petals. If it is an odd number it will have that amount of petals on the graph.
http://www.dreamcalc.com/dchelp/fxgraph_polar.gif
Lemniscates have two equations. They are: r^2
= a^2 sin 2 theta, and r^2 = a^2 cos 2 theta, where a doesn’t equal zero.
http://jwilson.coe.uga.edu/EMAT6680Su06/Byrd/Assignment%20One/image35.gif
This week we learned about polar and how to graph them. There are six types of polar graphs.
ReplyDeleteTypes of Polar graphs:
-Circle
-Limacons (snails)
-Cardioid
-Rose Curves
-Lemniscates
Circles:
There are two equations while dealing polar circles. The equations are r= a cos theta & r= a sine theta. (“a” is the diameter of the circle that has its left-most edge/bottom-most edge at the pole). This polar graph simply makes a shape of a circle.
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
Limacons (snails)
There are two equations. But this one has a +/-, a and b. Equations are r=a +/- b sin theta, where a>0 and b>0. Next one is r= a +/- b cos theta, where a>0 and b>0.
http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image024.jpg
Cardioid:
There are two equations. The number front of the plus and the the cos/sin are the same which is A. Equations are r= a+/-a sin theta, r= a+/- a cos theta. Example is like 2 +/- 2 sin theta = cardioid.
http://www.faculty.umassd.edu/adam.hausknecht/temath/TEMATH2/Examples/Assets/PolarTaylorPolynomials/Cardioid_stopped.gif
Rose Curves.
Graph that is produced from a polar equation in the form of : r=a sin ntheta or r=a cos ntheta, where a doesn’t equal to 0 and n is an integer>1. if n is a even integer, then the rose will have 2n petals if it is odd it will have n petals.
http://us.monografias.com/docs33/polar-coordinate/Image5617.gif
Lemniscates:
Containing the sine function will be symmetric to the pole while the lemiscate containing the cosine function will be symmetric to the polar axis, to theta= pi/2, and the pole. Equations are r squared= a squared sin 2theta or r squared= a squared cos 2theta, where a doesn’t equal to 0.
http://jwilson.coe.uga.edu/EMAT6680Su06/Swanagan/Assignment1/Asmt1prob10dpic3.gif
Spiral:
It a curve on the plane that never end which basically makes endlessly outward or inward sometimes it can do both.
http://www.mathamazement.com/images/Pre-Calculus/06_Additional-Topics-in-Trigonometry/06_04_graphs-of-polar-equations/logarithmic-spiral.jpg
This week we discussed polar and rectangular. We also learned polar graphs. The interesting thing about polar graphs is the unique shape they make. There are six different types of polar graphs. Each graph has its own shape and equation. The different types of polar graphs are as follows:
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://digilander.libero.it/roberto20129/matematica/img_curve/Limacon1.gif”>Limacon graph
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( my favorite) are the prettiest.
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”>Rose Petal Graph
4.The Cardiods
The cardiods are related to the limacons. A and b must be equal , or
A+Asin theta or B-Bsine theta
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png”>Cardiod Graph
5. The Lemniscates
r^2=a^2 sin 2θ or r^2=a^2 cos 2θ
“r^2” may also be represented as r=sqrt
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Perry/Assignment%201%20Distance%20Equations/Distance%20equations_files/image065.jpg”>Leminscates graph
6. The last are spirals :
Spirals are curves on planes that will turn in or out.
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs_files/image006.jpg”>Spiral Graph
:)
this week in advance math,we learned that there are six different polar graphs:Circles, Limacons, Cardioids, Rose Curves, Lemnisicates, and Spirals
ReplyDeleteCircles
r = acostheta
r = a sin theta
Cardioids:
r = a +/- a cos theta
r = a +/- a sin theta
Rose Curves:
r = a sin ntheta
r = a cos ntheta
We recieved a packet this week that had six different polar graphs in it:
Circles, Limacons, Cardioids, Rose Curves, Lemnisicates, and Spirals
Circles
r = a cos theta
r = a sin theta
(a is the diameter of a circle that has a left most/bottom most edge at the pole)
Cardioids:
r = a +/- a cos theta
r = a +/- a sin theta
Limacons (Snails):
r = a +/- b sin theta where a > 0 and b > 0
r = a +/- b cos theta where a < 0 and b > 0
Rose Curves:
r = a sin ntheta
r = a cos ntheta
Lemnisicates:
r2 = a2 sin 2theta
r2 = a2 cos 2theta
Spiral:
A curve on out.the plane that will turn in or out
Lemnisicates:
r2 = a2 sin 2theta
r2 = a2 cos 2theta
Spiral:
A curve on out.the plane that will turn in or out
Circle-Pictures:http://en.wikipedia.org/wiki/File:Circle_r%3D1.svg
Rose Curve- http://en.wikipedia.org/wiki/File:Rose_2sin(4theta).svg
Spiral-http://en.wikipedia.org/wiki/File:Archimedian_spiral.svg
Limacon- http://en.wikipedia.org/wiki/File:Limacons.svg
Lemniscate- http://en.wikipedia.org/wiki/File:Infinity_symbol.svg
Cardioid
http://en.wikipedia.org/wiki/File:CardioidCircleEnvelope.svg
http://en.wikipedia.org/wiki/File:CIRCLE_1.svg
We were introduced to polar graphs this week in Chapter 11. We will be tested and quized on these types of graphs and need to be able to recognize them. There are six different types of graphs: circle, cardiods, limacons, lemniscates, spirals, and rose curves.
ReplyDeleteThis website: http://www.mathwords.com/p/polar_curves.htm
will give you illustrations of the graphs by simply clicking the name of the polar graph you want to see.
The only polar graph they do not have an illustration to is the circle, but you can find a picture of the circle graph in the handout we got on Monday. It looks just like a circle. The equation for it is r= a cos theta. “a” can be any number. Be careful when there is no number infront of the cos or sin it could be understood as 1.
Cardiods:
R= a +/- a sin theta or r = a +/- a cos theta The “a’s” in the problem have to be the same number
Limacons:
R= a +/- b sin theta where a > 0 and b > 0 or r = a +/- b cos theta where a > 0 and b >0 The “a and b” have to be different numbers.
Rose curves:
R = a sin ntheta or r = a cos ntheta This graph will have an “n” before the theta. The number of loops depends on this number. If it is even, the number of loops is doubled, if it is odd, the number remains the same.
Lemniscates:
R^2 = a ^2 sin 2theta or r^2 = a ^2 cos 2theta You can tell these because the “r” is squared and there is a 2 in front of the theta.
This week in advanced math we got a packed that showed us the polar graphs and there formulas. Here are the different types of graphs we learned.
ReplyDeleteCircles in Polar form:
I learned the hard way that this is the name of this type of graph and not just a polar graph. When graphed this type of polar equation looks like a circle. The formula for this type of polar equation is r=a cos(theta) where "a" is the diameter of the circle that has its left most edge at the pole. The other formula is r=a sin(theta) where "a" is the diameter of the circle that has its bottom-most edge at the pole.
Limacons(Snails):
The formulas for Limacons are r=a+/- b sin(theta), where a>0 and b>0. and r=a+/- b cos(theta), where a>0 and b>0. If your answer is less than 1 you will have an inner loop.
Cardiods:
Based on the name you can tell that they are sort of a heart shape, but a distorted heart. Cardiods are like Limacons but they occur when you have the same number twice, like two a's instead of an a and a b. The formula is r=a+/- a sin(theta) and r=a +/- acos(theta)
Rose Curves:
Rose Curves occur when n is times theta. r= a sin n(theta) or r=a cos n(theta), where a is not equal to 0 and n is an integer > 1. They are called rose curves because they form loops that resemble petals.
Lemniscates:
Involves numbers being squared. r^2= a^2 sin 2(theta) or r^2= a^2 cos 2(theta), where a is not equal to 0.
You can find these pictures at http://www.mathamazement.com/Lessons/Pre-Calculus/06_Additional-Topics-in-Trigonometry/graphs-of-polar-equations.html or
http://www.tutorvista.com/answers/draw-the-graph-of-the-polar-equation-r-sin-2-theta-0-le-theta-le-2-pi/183217