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Mathematical Expression Editor
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Objectives:
1.
Review polar coordinates.
Recall that the transformation to get from polar coordinates to Cartesian
coordinates is
The picture relating to is shown below:
It is useful to note that .
The point corresponds to the Cartesian point
Remember that polar coordinates was great for describing certain objects,
such as circles.
Transform the equation into polar coordinates.
To
transform the equation into polar, we plug in , into the equation to
get
which means the equation is .
One issue we will encounter with polar is the non-uniqueness of points.
From now on, we will restrict ourselves to the situation where (i.e.
we will not look at negative -values). This will help us a little bit
later.
What does look like in Cartesian coordinates?
Transform the line into polar coordinates.
To transform the equation, we
plug in , to get
Since is just a point (and will not describe the whole line), we can divide by
to get
On the interval , this happens when
Therefore, the line can be described as and . Note that the former gives the
portion of the line with and the latter gives the portion of the line with
.
The line in polar coordinates becomes
The circle in polar coordinates becomes
Expand the circle to get , or . In polar, this is . Now solve for .
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)