M408D SPRING 2015 HOMEWORK #7 - cheatham (sc36975) HW07 um...

cheatham (sc36975) – HW07 – um – (53890) 1
This print-out should have 20 questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
001 10.0 points
Locate the points given in polar coordinates
by
P 4 ,
2
3
π , Q − 3 ,
1
2
π R 4 ,
1
3
π ,
among
2 4 − 2 − 4
2
4
10.0 points
Which, if any, of
A. (4 , π / 3) ,
B. (4 , 7 π / 3) ,
C. ( − 4 , 4 π / 3) ,
are polar coordinates for the point given in
Cartesian coordinates by P (2 , 2
√
3)?
5.
P :
Q :
R :
6.
P :
Q :
R :
For then the points
P 4 ,
2
3
π , Q − 3 ,
1
2
π R 4 ,
1
3
π ,
correspond to
P :
Q :
R :
in Cartesian coordinates.
keywords: polar coordinates, Cartesian coor-
dinates, change of coordinates,
002 10.0 points
Which, if any, of
A. (4 , π / 3) ,
B. (4 , 7 π / 3) ,
C. ( − 4 , 4 π / 3) ,
are polar coordinates for the point given in
Cartesian coordinates by P (2 , 2
√
3)?

cheatham (sc36975) – HW07 – um – (53890) 2
r = 4 and θ = π / 3, but there are equivalent
solutions for r < 0 as well as values of θ dif-
fering by integer multiples of π . For the given
choices we thus see that
A. TRUE: solution noted already.
B. TRUE: di ff ers from π / 3 by 2 π .
C. TRUE:
− 4 cos(4 π / 3) = 2 , − 4 sin(4 π / 3) = 2
√
3 .
003 10.0 points
A point P is given in Cartesian coordinates
by P ( − 1 , 1). Find polar coordinates ( r, θ ) of
this point with r < 0 and 0 ≤ θ < 2 π .
1. −
√
2 ,
5 π
4
2. −
√
2 ,
7 π
4
correct
3. −
√
3 ,
7 π
4
4. −
√
3 ,
5 π
4
5. −
√
3 ,
3 π
4
6. −
√
2 ,
3 π
4
Explanation:
Since the relationship between Cartesian
coordinates and polar coordinates is
x = r cos θ , y = r sin θ ,
the point P ( − 1 , 1) in Cartesian coordinates
can be given in polar coordinates as
P −
√
2 ,
7 π
4
,
004 10.0 points
Which one of the following shaded-regions
in the plane consists of all points whose polar
coordinates satisfy the inequalities
3 < r ≤ 4 ,
1
3
π ≤ θ ≤
5
6
π ?
1.
2 4
2.
2 4
3.
2 4
4.
2 4
5.
2 4
6.
2 4
correct