Derivative of a parametric circle
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If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Find
directly from the parametric equations
and evaluate
at
.
First, let’s discuss this function. What does its graph look like?
Help
A circle
What is its radius?
The radius is 3.
Where is the center?
At the origin.
Try to draw the graph from the parametric equations without using your graphing calculator. Then check by clicking “Next”.
alt="Graph of a circle. Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!
Locate the point for
and show the tangent line. Then check by clicking “Next”.
alt="Graph of a circle with a tangent line shown. Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!
What is the algebraic sign of the slope of the tangent line?
When a line slopes down to the right, it has a negative “rise” over a positive “run”. Its slope is negative.
What will be the algebraic sign of
at this point?
It also is negative.
Now let’s determine
from the parametric equations. State the general relationship among
.
Determine
Determine
Substitute these results in
.
Set up the evaluation of
.
How do we evaluate
on the calculator?
We determine
and take the reciprocal.
What “mode” does the calculator need to be in?
Radian mode.
Determine the decimal equivalent of
.
Is this consistent with the graph?
Yes, the tangent line is steeper than a line of slope = – 1.
Now let’s determine
from the parametric equations. State the general relationship between
.
Apply this to our result for
We get
.
Simplify this result.
Using
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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General Contents
Detailed Contents
Index