Click to see full answer Moreover, what is a Limacon graph? Subsequently, question is, why is it called a Limacon? The name ' limacon ' comes from the Latin limax meaning 'a snail'. When the value of a is less than the value of b, the graph is a limacon with and inner loop. When the value of a is greater than the value of b, the graph is a dimpled limacon. When the value of a equals the value of b, the graph is a special case of the limacon. It is called a cardioid. French word that means "snail," from Latin "limax," with reference to the shape of the snail's shell.
There is a cedilla on the c which means the c is pronounced as an s — David Quinn Apr 19 '17 at The lemniscate , also called the lemniscate of Bernoulli, is a polar curve whose most common form is the locus of points the product of whose distances from two fixed points called the foci a distance away is the constant. There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time.
Steps Understand how polar equations work. It will help your intuition. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?
Learn more. Asked 1 year, 1 month ago. Active 26 days ago. Viewed 1k times. When the value of a is greater than the value of b, the graph is a dimpled limacon. When the value of a is greater than or equal to the value of 2b, the graph is a convex limacon. When the value of a equals the value of b, the graph is a special case of the limacon.
It is called a cardioid. When the value of a equals the value of b, the graph is a special case of the limacon. It is called a cardioid. Notice that, in each of the graphs of the liamsons, changing from sine to cosine does not affect the shape of the graph just its orientation. Equations using sine will be symmetric to the vertical axis while equations using cosine are symmetric to the horizontal axis.
The sign of b will also affect their orientation. The graphs of equations of the form and will be lemniscates. This is a graph of the lemniscate of Bernoulli. This next graph is rather intriguing. After working with several polar graphs and observing their general shape, periodicity, and symmetry, it was quite surprising to end up with the graph of a straight line. To prove that this is actually the correct graph for this equation we will go back to the relationship between polar and Cartesian coordinates.
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