[nabs-l] Unit Circle

[Joseph C. Lininger]

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Well, I'm not sure exactly what you're needing. If you are asking for a
little bit of information on the unit circle, I've provided it below.
I've also given a basic suggestion for tactile things you can do to help
you visualize it if you need that.

The unit circle is a circle with a radius of 1 unit centered at the
origin (0,0) in the Cartesian coordinate system. . The term unit is
general, and depends on what units you're working with. Also, if you're
working in a different coordinate system, such as polar, the definition
changes slightly. Of course, polar coordinates are just circular
coordinates, so once you grasp the concept of a unit circle you won't
have any trouble with those. Anyway, I'm getting off track here.

If (x,y) is a point on the unit circle in the first quadrant in the
Cartesian coordinate system, then x and y are the lengths of the legs of
a right triangle with hypotenuse 1. This means the Pythagorean Theorem
holds. That is:

x ^ 2 + y ^ 2 = 1

The values for x and y can vary, but the hypotenuse will always be one
if the point is on the unit circle. Points on the unit circle can be
found in the other quadrants as well by taking negative x and/or y values.

That's the overview. If you remember that, then the work you do in
precalculous will be a lot easier.

As for tactile representations, you can draw one using a protractor as
has already been suggested. If you don't have one, you could draw an
approximation of a unit circle, enough to allow you to visualize it
anyway, using basic graphing techniques. To do this, what I suggest is
that you simply solve the Pythagorean Theorem for interesting values of
x and y. The ones you'll want to solve for include:

y = 1
y = -1
x = 1
x = -1

Also solve for some values between these. For example, solve for x = .5
and y = .5, as well as their negative equivalents. You can do this with
any degree of precision you want. Be very careful you keep the positive
values and negative values straight! It may seem silly to mention that
at this stage, but trust me it's a simple mistake to make when you start
squaring and adding repeatedly and some of the numbers are negative. If
you lose a sign, you'll start getting results like -1 = 1. LOL

Once you've got all the points you want, plot these points on a piece of
braille graph paper. Then draw a circle (using glue, string, a magic
marker, or something like that) that passes smoothly through all of
these points. If you do it right, you'll end up with a circle centered
at the origin which crosses the x axis at points (1,0) and (-1,0), and
which crosses the y axis at (0,1) and (0,-1).

If you need further assistance, don't hesitate to ask. Unit circles are
actually pretty interesting in mathematics, although they probably don't
seem like it while you're first learning about them. I didn't think so
when I took precalculous, anyway.
- --
Those of you who think they know everything are very annoying to those
of us who actually do.
Joseph C. Lininger, <jbahm at pcdesk.net>
Kayleigh Joiner wrote:
> Hello listers,
> This is Kayleigh from Texas. I am currently taking pre-calculus and we have started covering the unit circle. I am not aware of anything that is available for the blind concerning this topic. If anyone has any suggesstions they would be greatly appreciated.
> Sincerely,
> Kayleigh 
> 
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