gonzales (pag757) – HW 07 – Odell – (57000)
1
This printout should have 30 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
Locate the points given in polar coordinates
by
P
p
2
,
2
3
π
P
,
Q
p

3
,
1
2
π
P
R
p
2
,
1
3
π
P
,
among
2
4

2

4
2
4

2

4
b
u
b
c
r
u
t
r
s
1.
b
u
t
b
c
P
:
Q
:
R
:
2.
b
u
t
b
c
P
:
Q
:
R
:
3.
b
u
t
b
c
P
:
Q
:
R
:
4.
b
u
t
b
c
P
:
Q
:
R
:
5.
b
u
t
b
c
P
:
Q
:
R
:
correct
6.
b
u
t
b
c
P
:
Q
:
R
:
Explanation:
To convert From polar coordinates to Carte
sian coordinates we use
x
=
r
cos
θ ,
y
=
r
sin
θ .
±or then the points
P
p
2
,
2
3
π
P
,
Q
p

3
,
1
2
π
P
R
p
2
,
1
3
π
P
,
correspond to
b
u
t
b
c
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
,
4
π/
3)
,
B. (4
, π/
3)
,
C. (4
,
13
6)
,
are polar coordinates For the point given in
Cartesian coordinates by
P
(2
,
2
√
3)?
1.
A and B only
correct
2.
A only
3.
C only
4.
B and C only
5.
A and C only
6.
B only
7.
all oF them
8.
none oF them
Explanation:
To convert From Cartesian coordinates to
polar coordinates we use the relations:
x
=
r
cos
θ ,
y
=
r
sin
θ ,
so that
r
2
=
x
2
+
y
2
,
tan
θ
=
y
x
.
±or the point
P
(2
,
2
√
3) in Cartesian co
ordinates, thereFore, one choice oF
r
and
θ
is