Module 10 Lesson 3: Practice
Problems:
1. State three other coordinates (within one rotation) for the following polar point:
(3, /3)
2. State three other coordinates (within one rotation) for the following polar point: (2, 2/3)
3. State three other coordinates (within one rotation) for the following polar point:
(6, -5/6)
4. State three other coordinates (within one rotation) for the following polar point: (4, -3/2)
5. This is a graph of:
6. This is a graph of:
7. This is a graph of:
8. This is a graph of:
9. For the polar equation r=sin4, the graph follows which quadrant order when
graphing by hand?
10.
When graphing a lemniscate by hand, you must remember to:
11.
When graphing a spiral by hand, you should:
12.
When graphing a rose by hand, you should:
Solutions: A is correct for all (shuffle answers)
1
2
3
4
5
6
7
8
9
10
A
(3, -5/3)
(-3, 4/3)
(-3, -2/3)
(-2, 4/3)
(2, 5/3)
(2, -/3)
(6, 7/6)
(-6, /6)
(-6, -11/6)
(-4, /2)
(4, 3/2)
(4, -/2)
Limacon
Lemniscate
Rose
Spiral
Q1, Q3, Q2, Q4
Graph a positive
and negative r
B
(3, -5/3)
(3, 4/3)
(3, -2/3)
(2, 4/3)
(2, 5/3)
(2, -/3)
(6, 7/6)
(6, /6)
(6, -11/6)
(4, /2)
(4, 3/2)
(4, -/2)
Lemniscate
Limacon
Lemniscate
Lemniscate
Q1, Q2, Q3, Q4
Use the positive
value only
C
(3, 5/3)
(-3, 4/3)
(-3, 2/3)
(-2, 4/3)
(2, 5/3)
(2, /3)
(6, 7/6)
(-6, /6)
(-6, 11/6)
(-4, /2)
(4, 3/2)
(4, /2)
Rose
Rose
Limacon
Rose
Q1, Q4, Q3, Q2
Use the negative
value only
11
Choose small angle Choose large angle
values
values
Only graph from
0<<2
12
Plot the points in
order and connect
the points as you
go along
Only plot from
0<< then reflect
the dots about the
x-axis
Plot the points in
order and connect
them after you
have completed
one rotation
D
(3, 5/3)
(-3, 4/3)
(-3, -2/3)
(-2, 4/3)
(2, 5/3)
(2, /3)
(6, 7/6)
(-6, /6)
(-6, 11/6)
(-4, /2)
(4, 3/2)
(4, /2)
Spiral
Spiral
Spiral
Limacon
Q1, Q3, Q2, Q4
Square the right
side to get the
value of r
Plot the first few
points and then
eyeball it from
there
Copy the graph
from a calculator.