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A lemniscate graph is seen in real life with ribbons

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lemniscate : looks like ribbon

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r^2 = a^2 cos 2(theta)
r^2 = a^2 sin 2(theta)

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Spiral of Archimedes
r=a(theta)
theta in radians

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The infinity symbol is an example of a lemiscate graph in real life

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Cardioid microphones: focuses on picking up sound from one direction. This type of microphone would be used in terview or at the ticket booth in movies.

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Cardioid: cardioid graph looks like heart
r=a+a cos(theta)
r=a+a sin(theta)

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Polar Vocabulary
The spiral of Archimedes is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant angular velocity. Equivalently, in polar coordinates (r, θ), it can be described by the equation r = aθ.

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Cardioid
r=a+acos(theta)
r=a+asin(theta)

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A clock is an example of a limacon graph.

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Daisy is a real life example of Rose graph

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A snail's shell....

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Polar graphs can be better than Cartesian graphs when one wants to graph something on a round shape, such as a sphere.

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A tornado is a real life example of the Spiral of Archimedes

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An example of a leminscate graph is a figure 8.

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(4, -30)
(-4, 150)

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A spiral of Archimedes graph in real life could be seen in a snail's shell.

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A lemniscate graph can be seen in real life when figure skating is happening in figure 8s.

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limaçon: the graph of a polar equation of the form
r=a+bcos(theta) or
r=a+bsin(theta)
where a and b are both positive.

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Shells are a real life example of the spiral of Archimedes

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A cardioid graph is in a shape of a heart which can be turned in is side if needed. Also hearts are a real life example of a cardioid graph,

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nautilus shell

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a heart is an example of cardioid graphs in real life.

a heart is an example of cardioid graphs in real life.

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Galaxies are an example of real life spiral of Archimedes graphs

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rose: a graph shaped like a daisy with an equation of r=acosnx or r=asinnx

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Polar graphs are better than Cartesian in certain cases like when you are trying to graph something on the earth. (I accidentally wrote in the comment section D: )

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Limaçons appear through light through round glass

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When you are measuring something on the globe or in a circular area.

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Given the coordinates (4, 330), what are some equivalent coordinates

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Given the coordinates (4, 330), what are some equivalent coordinates