Calculus Maximus WS 8.1: Polar Intro & Derivs
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Worksheet 8.1—Polar Intro & Derivatives
Show all work. No calculator except unless specifically stated.
Short Answer
Convert the following equations to polar form.
1.
4y
2.
35 20xy
3.
22
25xy
Convert the following equations to rectangular form.
4.
3secr
5.
2sinr
6.
5
6
For the following, find
dy
dx
for the given value of
.
7.
23sinr

,
3
2
8.
31 cosr

,
Calculus Maximus WS 8.1: Polar Intro & Derivs
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9.
4sinr
,
10.
2sin 3r
,
11. Find the point of horizontal and vertical tangency for
1sinr

. Give your answers in polar form
,r
.
Calculus Maximus WS 8.1: Polar Intro & Derivs
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Make a table (of values, not one at which to eat) and sketch the graph.
12.
22sinr

13.
12cosr

14.
4cos 2r
15.
2
4sin 2r
Multiple Choice
16. If
0a
and
0
, all of the following must represent the same point in polar coordinates except
which ordered pair?
(A)
,a
(B)
,a

(C)
,a


(D)
,a


(E)
,2a

Calculus Maximus WS 8.1: Polar Intro & Derivs
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17. Which of the following gives the slope of the polar curve
rf
graphed in the xy-plane?
(A)
dr
d
(B)
dy
d
(C)
dx
d
(D)
/
/
dy d
dx d
(E)
dy dr
dx d
18. Which of the following represents the
graph of the polar curve
2secr
?