General Contents
Detailed Contents
Index
Graph of Polar Coordinates
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We wish to graph the point with polar
coordinates
.
General Contents
Detailed Contents
Index
Which coordinate should we consider first?
It usually is easier to determine the ray for the angular coordinate first.
What fraction of a complete circle is
radians?
Since a full circle consists of
radians, we have
,
or the angle is
of a full circle.
Use this information to draw a graph on paper of the ray at
. Then check your work by clicking “Next”.
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How do we handle the value of
r
?
We measure
r
along this ray.
Do that on your diagram for this
r
= 3.
Then check your work by clicking “Next”.
For positive 3, we measure in the positive direction along the ray:
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Add a ray at a position which is a half a circle further around the pole. That is, add 180 degrees =
p
radians to get
the
position of the new ray.
Then check your work by clicking “Next”.
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If we want to use this new ray to specify the plotted point, what measurement do we need to make along it?
We need to measure 3 units in the negative direction on this ray.
Show this in your diagram. Then check your work by clicking “Next”.
The – 3 units is shown in red.
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If we use this ray, what are the polar coordinates of this point?
We have illustrated the use of positive and negative values of
r
with positive angles to specify the same point. Can we also use negative values of the angle?
Yes.
Show a negative angle for a ray in the first quadrant for this same point in your diagram. Label the angle.
Then check your work by clicking “Next”.
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What is the value of the angle?
State the polar coordinates of this point using this negative angle.
Can we also describe this point with negative values of both
r
and
q
?
Yes.
Show a negative angle which requires a negative value of
r
.
Then check your work by clicking “Next”.
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Determine the angle.
Give the coordinates of the point using this angle.
The point is
Summarize these ways of specifying the same point.
The following are equivalent ways of specifying this point.
,
,
,
In specifying the angle, must we always use the symbol
p
?
No, we can use a decimal approximation
of
p
.
Express
in terms of a decimal approximation.
With
p
= 3.14, we get
,
so the coordinates of the point can be also written as (3, 0.79)
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
.