Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.
Infinite Precalculus - Intro to Polar Form Notes › uploads › 5 › 7 › 6 › 4 › 57648445...
14
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Transcript of Infinite Precalculus - Intro to Polar Form Notes › uploads › 5 › 7 › 6 › 4 › 57648445...
©V s2B0s1Z8B cKOu^t^aZ [SMoffhtpweawrEev RLCLXCY.B _ DAElclR prQingqhAtDsv LrNeysueWrqvleAdH.f A yM\aJdOeF ywWiItchO fI\nCfLilnViPtYeb vPGrleqcWaAlycVualSujsZ.
Worksheet by Kuta Software LLC
BC Calculus
Intro to Polar Form Notes
Name___________________________________
Date________________ Period____
©m d2D0V1m8h NKNutt_an lSWobfctnwIaOr^eb ILNLMCG.T V nAplrlh Hrrisg^hFtdsu BrLeDs[eZrkvieDdt.
-1-
Plot the point with the given polar coordinates.
1) (-2, 5p
6 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
2) (3, -7p
12 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
Find 3 other polar coordinates that describe the same point as the provided polar coordinates.
3) (3, -11p
6 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
4) (-1, -p
4 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
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-2-
Convert each pair of polar coordinates to rectangular coordinates.
5) (4, -11p
6 ) 6) (-2, 4p
3 )
Convert each pair of rectangular coordinates to polar coordinates where r > > 00 and 00 £ £ qq < < 22pp .
7) (-2, 2 3) 8) (- 2 , - 2)
Consider each polar equation. Classify the curve; and sketch the graph.
9) r = 5
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
10) r = 4sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
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Worksheet by Kuta Software LLC
-3-
11) r = -7cos q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
12) r = 3 + 3cos q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
13) r = 4 + 3sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
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-4-
14) r = 3 - 3sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
15) r = 2 + 4sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
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Worksheet by Kuta Software LLC
-5-
16) r = 4sin (3q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
17) r = 2cos (5q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
18) r = 2sin (2q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
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-6-
Convert each equation from rectangular to polar form.
19) y = -x 3 20) y = 5x
21) (x + 3)2 + (y - 1)2
= 10 22) y = x2
3
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Worksheet by Kuta Software LLC
-7-
Convert each equation from polar to rectangular form.
23) q = 3p
4
24) r = 4cos q + 2sin q
25) r2 = 4csc (2q ) 26) r2
= 3sec (2q )
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Worksheet by Kuta Software LLC
BC Calculus
Intro to Polar Form Notes
Name___________________________________
Date________________ Period____
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-1-
Plot the point with the given polar coordinates.
1) (-2, 5p
6 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
2) (3, -7p
12 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
Find 3 other polar coordinates that describe the same point as the provided polar coordinates.
3) (3, -11p
6 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
(3, -11p
6 + 2np) and (-3, -
11p
6 + (2n + 1)p)
where n is an integer
4) (-1, -p
4 )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4
(-1, -p
4 + 2np) and (1, -
p
4 + (2n + 1)p)
where n is an integer
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Worksheet by Kuta Software LLC
-2-
Convert each pair of polar coordinates to rectangular coordinates.
5) (4, -11p
6 )(2 3 , 2)
6) (-2, 4p
3 )(1, 3)
Convert each pair of rectangular coordinates to polar coordinates where r > > 00 and 00 £ £ qq < < 22pp .
7) (-2, 2 3)
(4, 2p
3 )8) (- 2 , - 2)
(2, 5p
4 )
Consider each polar equation. Classify the curve; and sketch the graph.
9) r = 5
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Circle
10) r = 4sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Circle
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Worksheet by Kuta Software LLC
-3-
11) r = -7cos q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Circle
12) r = 3 + 3cos q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Cardioid (Limaçon)
13) r = 4 + 3sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Dimpled limaçon
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Worksheet by Kuta Software LLC
-4-
14) r = 3 - 3sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Cardioid (Limaçon)
15) r = 2 + 4sin q
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Looped limaçon
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Worksheet by Kuta Software LLC
-5-
16) r = 4sin (3q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Rose
17) r = 2cos (5q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Rose
18) r = 2sin (2q )
0
p
6
p
3
p
22p
3
5p
6
p
7p
6
4p
3 3p
2
5p
3
11p
6
1 2 3 4 5 6 7
Rose
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Worksheet by Kuta Software LLC
-6-
Convert each equation from rectangular to polar form.
19) y = -x 3
q = 2p
3
20) y = 5x
tan q = 5
21) (x + 3)2 + (y - 1)2
= 10
r = -6cos q + 2sin q
22) y = x2
3
r = 3tan q sec q
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-7-
Convert each equation from polar to rectangular form.
23) q = 3p
4
y = -x
24) r = 4cos q + 2sin q
(x - 2)2 + (y - 1)2
= 5
25) r2 = 4csc (2q )
y = 2
x
26) r2 = 3sec (2q )
x2 - y2 = 3
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