# Analyzing Circles On The Coordinate Plane

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```Make some observations and answer the questions
in your composition book.
1.
Did you use vertical and horizontal lines to help
you? If so, how?
2.
What did you notice while filling out the table?
3.
What did you wonder when you were filling out
the table?
4.
Is there a y-coordinate that I could have filled in
that would have given only one answer to the xcoordinate? If so, what is it? Are there any others? If
not, what is your reasoning?
5.
Is there a slope that I could have filled in that
would have given only one answer to the x-coordinate?
Are there any others? If so, what is it? Are there any
others? If not, what is your reasoning?
6.
If I gave you the x-coordinate and no unit circle
diagram, can you think of a way to get the ycoordinate? If you need a hint, look at the footnote.1
7.
If I gave you the slope of the angle and no unit
circle diagram, can you think of a way to get the xcoordinates and the y-coordinates?
8.
If I gave you the x-coordinate and no unit circle
diagram, can you think of a way to get both angles?
1
The sum of the squares of…
Analyzing Circles on the Coordinate Plane
What is the radius of the above circle? _______ units.
Therefore we call this a unit circle.
You’re going to practice using a protractor and
estimating coordinates on the circle.
Let the point (1, 0) represent 0 degrees, (0, 1) represent
90 degrees, (-1, 0) represent 180 degrees, and (0, -1)
represent 270 degrees.
The forward problem. Since you are estimating, and
the diagram is labeled to the tenths, you are going to
estimate to the hundredths.
Estimate the following coordinates/slopes. We will
compare the true answers to your estimations in a
couple of days.
angle
23
48
75
105
154
185
227
300
x-coordinate
y-coordinate
slope of
angle
The backward problem. You are given one piece of
information. It turns out that with that one piece of
information, you can get all the other values. In fact,
with that one piece of information, you can get two
different sets of answers!
angle
(a)
(b)
x-coordinate
y-coordinate
0.30
(a)
0.77
(b)
(a)
1
(b)
(a)
0.30
(b)
(a)
(b)
(a)
(b)
(a)
(b)
slope of
angle
-1.23
-0.89
-0.62
(a)
-0.20
(b)
```