Lab 09
Name:
Start time:
Number of questions:
11
This set of questions goes with the pages of applets and activities for Lab 09. Use the applets and activities there to answer the questions.
Question 1 (1 point)
What is the polar graph of sin(t)?
a.
A circle of radius 1 centered at the origin.
b.
A circle of radius 1/2 centered at (0,1/2).
c.
A circle of radius 1/2 centered at (0,-1/2).
d.
A circle of radius 1/2 centered at (1/2,0).
e.
A circle of radius 1/2 centered at (-1/2,0).
Question 2 (1 point)
Set the grapher to start when
t
= 0. What ending value of
t
is the smallest you need to have the entire circle traced?
a.
Pi/4
b.
Pi/2
c.
Pi
d.
2*Pi
e.
4*Pi
Question 3 (.5 points)
Graph sin(
n
*
t
) for various integer values of
n.
Make a conjecture about the number of "petals" on the "rose."
a.
n petals
b.
n petals if n is even, 2*n petals if n is odd
c.
n petals if n is odd, 2*n petals if n is even
d.
2*n petals
Question 4 (.5 points)
Graph cos(
n
*
t
) for various integer values of
n.
Make a conjecture about the number of "petals" on the "rose."
a.
n petals
b.
n petals if n is even, 2*n petals if n is odd
c.
n petals if n is odd, 2*n petals if n is even
d.
2*n petals
Question 5 (1 point)
The graph of 1-sin(
t
) is called a cardioid, because it is heart shaped. Find the polar equation of another cardioid, whose graph is shown below.
a.
1 - sin(
t
)
b.
1 + sin(
t
)
c.
1 - cos(
t
)
d.
1 + cos(
t
)
Question 6 (.5 points)
The graph is symmetric with respect to the polar axis. What does this say about the algebraic symmetry of the function?
a.
r(t) = r(-t)
b.
r(t) = - r(t)
c.
r(t) = r(Pi/2 - t)
d.
r(t) = r(Pi - t)
Question 7 (.5 points)
A graph is symmetric with respect to the vertical line corresponding to
t
= Pi/2. What does this say about the algebraic symmetry of the function?
a.
r(t) = r(-t)
b.
r(t) = - r(t)
c.
r(t) = r(Pi/2 - t)
d.
r(t) = r(Pi - t)
Question 8 (1 point)
Be a little bit artistic here.
sin(t)*cos(3*t)
-->
Choose match
butterfly
fish
spider
sin(t)*cos(2*t)
-->
Choose match
butterfly
fish
spider
sin(t)*cos(5*t)
-->
Choose match
butterfly
fish
spider
Question 9 (1 point)
Think about what the graph of
r
(
t
) =
t
might look like before you try to graph it. What happens to the graph if you allow negative values of
t
?
a.
It is a circle, with symmetric values for negative t.
b.
It is a parabola, with symmetric values for negative t.
c.
It is a spiral, opening out in the opposite direction for negative t.
d.
It is a cross between a fish and a spider, and is not defined for negative t.
e.
It is a rose with more and more petals, whether t is positive or negative.
Question 10 (1 point)
I wrote the polar grapher using what are called parametric plots, which treat both
x
and
y
as depending on
t
. If you look at the "fine print" at the bottom of the grapher you can see the formulas for how
x
and
y
points are being generated. What is the recipe I use?
a.
It is based on the conversion formulas from polar to rectangular coordinates, with r given by the polar function of t that is being plotted.
b.
It is based on the conversion formulas from rectangular to polar coordinates, with x and y computed by the Pythagorean theorem.
c.
It comes from the metric system.
d.
It comes from the reciprocal identities.
e.
It is based on solving quadratic trig equations to determine x and y.
Question 11 (2 points)
The "vertical line test" can be used to decide if the graph of a given cartesian equation in rectangular coordinates
x
and
y
represents a function. Explain in a sentence or two why the vertical line test doesn't apply for graphs of polar functions.
Equation
Create new equation
Number of questions: 11