Ndrne
Date
_
WORKSHEET
_
NON-CALCULA TOR
For each point (r, e , give rectangular coordinates (x,
Period_
15. (4,23")
- POLAR COORDINATES
NON-CALCULATOR
Plot each point.
v
1. A(2,~)
3.
c(-5.~)
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16. (-3,~)
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x=
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-3
s,n
~-30)
s:::; -3(1)
..
(~~)
5 E(5.21l)
,
,
For each point (} _,Y)
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19. (2,2)
I.
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:;~fi,
1- --\
~~~.:-~~
Name each pomt two ways using
polar coordinates where 2n:< 6 < 4n:
~)
,(-I)
~rt' 4-~
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13. I =(\)
~
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14.
J=(2j ~,&i:)
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coordinates (r, 0),
(1)
s
20. (5. 0)
Why;;;' ~ li.: radians
~
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5
,
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\.
For each poi t (x, y), give polar coordinates (r, 0), where () is in radians.
27. (-6,17)
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28.
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~
Name
Date.
_
Penod __
6.
r = -coso
5.
e = _ 3rc
4
WORKSHEET - SIMPLE POLAR GRAPHS
Non-Calcu lator
Identify and graph each polar equation.
1. r
=4
C \'f d.e
2.8=
2rc
3
(1) n:.\e.4
7. r=-4sinO
3. r = 3 sm 0 .
~C._.(",-r(_G_\-=-{.=-_
4. rsin8 = 4
'nbf~\
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J~1"1U{,.1
9 rcosO--2
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10. r=2cos8
Write the equation for each graph.
11.
C ::;-5 Cos. Q
12.
Plot each point and wnte three other polar coordinates for the point where
-27r s 8 :5 2)[.
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17.A(-3.i)
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19. C (-2,- 23"J
14.
'ffd
15.
a ~ : -;;2.
r::- '+
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Name
__
WORKSHEET:
Dale
_
A 9-3
Period__
6. r=2-sinO
1. r
= 3 + 3sin8
~.
graa~ on
(
.. I
7. r = 1 + 4sinO
CARDIOIDS AND LlMACONS
.Y~r
Graph each equation without usmq a calculator and name the type of
graph. Check y~r
.
U~6n
0l
calculator.
2. r
.
= 2 + 3cose
~
ffi~on
.
I
\ll~
If """"
Y"
\
8. r=3slnO
3. r = 5 - 2sinO
4. r
= 3-
3cosO
C A.V'C\lo
C\fUe
9. r
=4-
3coso
"J'axbu.\ \,(\e
,1~\
5 r=
2_+ 5sInO
UtAA,'i
1..\ rou ~ L)(\
I
11. rcos9=-5
.
.,'
<
6 (l
WJ~
I
,
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,t
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A 9-3
UrrA~O(l y}1~
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.
,
I
12.r=-6
C·\(C\e.
13. ti-
n
4
Li()L
I
A 9-3
I
I
CALCULATOR
For (r, 9), give rjCtangular coordinates (x, V). (8 is given in radians)
t. ~(,I~ I - ;B I ')
20. (n, 3.75)
X-=
J2 ~S
i ~.JZ
:SIt'S;;
«5\('\ ~~$'
::
For (x, V), give two sets of polar coordinates (r, 0), where 0 s 0 s 21[.
21. (12, -5)
(,,?) - 39)
c
~ (\~Lt(-5)i
1l-\4
\ U,fl
il
-\-~s ,
z:
fW1
e: ~t2. -::-
I ~~
z 13
L{
A 9-3
I
Name
__
Date.
_
A 9-4
Period __
r = 4cos20 Lerrn'l \<;c&..}e.
6.
WORKSHEET:
7. r = 4 - cosO
L\ffiCl.
ROSE CURVES AND LEMNISCATES
Graph each equation without using a calculator and name the type of
graph. Check YOLKgraph on your calculator.
1. r
= 3cos39
Kt>5e
-3 fi'~
2. r
= 3sin2e
if ~~
~
9.r=2
C! J"{,.\~
\
3. r
= 4cos 40
~OS'
~\
~
4.
r = 9sin26 Lerom Sa:U<.
<,
10. r = 2 + scosa
,
,
i ~
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uq,
11.
e = - 3~
4
'i
Q (..
n
12. 0 = _ 76n
---,--'_-I
0_e..__
13. rSln9=-3
k('l01\J
A 9-4
,--I
_A_9-4__.
It'..t-
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14_ r = 1 + 3sin8 ~j
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